An interesting paper I’ve recently found, by Kirill Reshetnikov from 2011: “Новые этимологии для прибалтийско-финских слов”, Урало-алтайские исследования 2 (5): 109–112. A Russian-only journal is a slightly odd location for publishing research on Finnic etymology, but I suppose technically still fair.
Two of his four comparisons I was already aware of, and I have no major complaints about them:
- Finnic *kasvot (plurale tantum) ‘face’ ~ Samoyedic *kat ‘face’ < PU *kas-
I’ve noticed on my own the possibility of connecting these words as well. The previous suggestions that I have seen for deriving the Finnic word from *kasva- ‘to grow’ have struck me as semantically forced. What I am not sure of, though, is reconstructing *kaswV as the common Proto-Uralic form. While loss of *w in consonant clusters would be regular in Samoyedic, there are no precedents for clusters of obstruent + semivowel in PU,  and also the loss of a stem vowel in Samoyedic after an original consonant cluster would be exceptional. Perhaps the root is simply *kasə, and *-vo- in Finnic is a suffix or two. 
- Finnic *oh-ut, *oh-kainen ‘thin’ ~ Ob-Ugric *waaɣəɬ ‘thin’  < PU *wokšə
Seemingly independently also proposed by Ante Aikio in the 2nd volume of his recent Studies in Uralic Etymology article series. Multiple non-trivial developments are involved, but the etymology still appears to be entirely regular.
while one comparison I remain hesitant on: North Finnic *turkki ‘fur coat’ ~ Samoyedic *tər ‘fur’. A three-consonant cluster *-rkk- would not be possible for PU; yet an analysis of the Finnic form as something like *tur-kka-j or *turk-ka-j, as Reshetnikov proposes, would seem unusual as well. There are some Finnic roots analyzable as *CVC-ka, I think a few might be analyzeable as *CVw-kka or *CVj-kka, and there’s even *po(n)č-ka ‘shank’, derived from PU *pončə- ‘tail’ — but most of the time “heavy” consonant-stem formations still seem to only involve dental suffixes. Another morphological reason to be suspicious is that the Finnic word is an unalternating *i-stem, a root type usually found in loans. True, some words of this type are old *j-derivatives (e.g. *kota ‘house’ → *koti ‘home’), but in those cases the underived root seems to be almost always still around as well.
Phonologically, I also do not think the development of PU *u to Samoyedic *ə can be considered normal in a consonant-stem root.
Interestingly however, no root for ‘fur’ or ‘fur coat’ seems to have been reconstructed for PU previously (despite a wide number of roots reconstructed with the meaning ‘skin’ ), nor even for Proto-Finnic proper; so perhaps that counts as a small point in favor of the etymology.
But mooving on to Reshetnikov’s last, and most interesting, proposal: Finnish/Karelian huoma- ‘possession, care’ (mostly in adverbs) ~ Hungarian óv ‘to protect, guard’. This seems like a good catch. Pre-Hungarian *-w has generally been vocalized word-finally (in words like *köw(ɛ-) > kő : köve- ‘stone’, *low(a-) > ló : lova- ‘horse’, *saw(a-) > szó : szava- ‘word’, *taw(a-) > tó : tava- ‘lake’), so a word-final -v like this would probably come from earlier *-β; which, in turn, is in inherited vocabulary perhaps more often than not from an earlier *m (in words like PU *nimə > név ‘name’, PU *ńälmä > nyelv ‘tongue’, Ugric #äľmV > enyv ‘glue’). 
Previously a different etymology for huoma has been proposed: borrowing from Germanic *sōmijan- ‘to fit; to honor’. The common Finnic verb *hoomat- ‘to notice’, and some derivatives such as Fi. huomio ‘attention’ probably do come from this source — but I agree that ‘possession’ is not an obvious development from this meaning at all.
Alas, at this point Reshetnikov seems to skip over some work. Observing that both Finnic and Hungarian have a long mid back vowel *oo / ó, he simply proceeds to reconstruct PU *šoma/*šooma. This was a paper released back when the idea of long vowels in Proto-Finno-Ugric was still mostly unchallenged — but even then, as far as I know, Hungarian ó has never been considered to descend from earlier *oo or *o! Most cases rather have í (e.g. ín ~ PF *sooni ‘vein, sinew’; nyíl ~ PF *nooli ‘arrow’) or a, á (e.g. nyal ~ PF *noolë- ‘to lick’; három ~ PF *kolmë(t) ‘3’; ház ~ PF *kota ‘house’). A short o in possible correspondence to Finnic *oo does appear in orr ‘nose’ ~ Finnic *voori ‘mountain’, and some examples of o ~ *o are known too.
But when it comes to Hungarian long ó, it seems that this is in all cases a secondary vowel resulting from vocalization of coda *w (when following pre-Hungarian *a and *o). The v-stems such as ló, szó, tó mentioned above demonstrate the process well. Other examples where the same can be assumed within a root include PU *kuŋə > hó ‘moon’. Hence the common PU root should be rather reconstructed as something like *šowə-ma, *šoxə-ma, *šoŋə-ma or *šuwa-ma, with the Finnic and Hungarian long vowels both resulting from contraction. Of these, I think the last option looks the best: as the *ma-derivative seems to date to PU already, the *ə-stem variants would have been at a risk of reduction to a consonant-stem formation *šoGma, from which we’d rather expect Finnic **houma or **huuma.
Finnic-internal evidence supports an analysis as a derivative as well. Beside huoma-, there exists also a largely parallel huosta- ‘possession, custody’; again attested only from Finnish and Karelian. The two are analyzeable as derivatives from a common root *hoo- (although -sta- is a rare formant; it usually derives local nouns, such as Fi. alusta ‘base’), which would probably have been a verb meaning approx. ‘to take care of’.
I suspect there’s even a third derivative of this hypothetical verbal root *hoo- to be found in Finnic, hidden in plain sight: *hoolë- ‘to take into custody, to take care of’ (not retained as an underived verb, only as several parallel derivatives, e.g. Fi. huolehtia, huolia, huolita). This has normally been analyzed as identical to the homophonic noun root *hooli ‘worry, bother’ (probably ← Baltic), but the semantics of this derivation seem to be a bit off. In that case, the morphology would also point to the bare root being treated both as a noun and a verb, which is attested in some old inherited words (e.g. *tuuli ‘wind’ : *tuulë- ‘to be windy’) — but I don’t think I’ve ever seen a case of this in loanwords, where instead dummy verbal suffixes are often piled on even for no reason whatsoever (e.g. *he-i-ttä- ‘to throw’, and not **hee-, from Germanic *sēa- ‘to sow’). Thus, an analysis as an old frequentative *hoo-lë- seems to work better.
Later on, this and ‘worry’ have probably semantically bled into each other, leading to e.g. Fi. huolehtia meaning both ‘to take care of’ and ‘to worry about’; or huolia meaning both ‘to take into custody’ and ‘to bother taking’.
If we can therefore establish a PU verb root *šuwa- ‘to take care of’, this also opens one interesting possibility. The common Samoyedic verb for ‘to give’ is reconstructed as *tə- (compare Nganasan ta-, tə-, Selkup *tatə-; but Tundra Nenets tā-). Unsurprizingly, it has been considered a reflex of PU *toxə- ‘to give’; but the development *o > *ə would be quite irregular.  On the other hand: the regular PU source of *ə is *u-a; and we expect *-w- to be lost in Proto-Samoyedic, so *šuwa- would seem to be a potential proto-form for this verb. An open stem vowel *-a- is, again, not expected to be lost, but if we reconstructed *təå- or *təə-, with a later contraction to *a or *å (in some forms?) in some languages, this might even explain the irregular long ā in Nenets  and open a in Nganasan.
The semantics, I admit, do not match very well at all. But an interesting further formation is the synonymous PSmy *tə-tå- ‘to give’. For this, a derivation from *šuwa- ‘to take care of’ would not be too odd; a causative derivative ‘to give in someone’s care’ could perhaps develop into a neutral word for ‘to give’. If it would make sense for this meaning to then propagate back to the base root is on the other hand a more difficult question.
— One last question to explore might be if this PU root has anything to do with PIE *h₁su- ‘good’, but that would run into a bit too many questions and tangents to be fruitful to get into right now.
 The “spirants” *d₁, *d₂ that can be found in a few roots like *käd₂wä ‘female animal’ do not count, I think; phonotactically they seem to behave more like liquids.
 I have recently developed a suspicion that there might exist an old obsolete noun-deriving suffix *-wa in a couple other Finnic words as well. One case that seems clear is *päivä ‘day, sun’, in light of an observation due to Janne Saarikivi: only *päj(ə)- should be considered a part of the original root, given several other words that appear to be related. In the UEW we can find some listed under the roots *päjä ‘fire’, *päjV ‘white, to gleam’; also relevant is Estonian päike ‘sun’, which cannot be derived from anything like **päiväkkä.
— As a further aside, this analysis moreover seems to show that the word is not actually an exception to the sound law *ä-ä > Finnic *a-e, which as of recently has been subject to ongoing discussion by at least Kallio, Zhivlov, and Aikio.
 *wooɣəθ according to László Honti; however, as I might have remarked before, I am skeptical of Honti’s *aa, which almost never seems to appear in Uralic vocabulary; and of his phonetically backwards sound change *oo > Mansi *aa. It seems more probable to me that if a separate Proto-Ob-Ugric stage existed, then its *aa was simply retained in Mansi, raised to *oo in Khanty. Commenting also on the reconstruction scheme of Eugene Helimski and Mikhail Zhivlov, where this vowel correspondence is reconstructed as short *a, would take me too far off the track here though.
 Reasonably well-reconstructible cases include: *čomčə ‘skin layer’ (S, Kh) | *iša ‘skin’ (S, F, P, ?Mo, ?Ma) | *ketə ‘skin’ (S, F, Mo, Smy) | *kopa ‘skin, bark’ (F, Ma, P, Smy) | *küpsɜ ‘skin on paws’ (P, Ms, Kh) | *perə ‘skin’ (Kh, Smy) | *śuka ‘bark / skin?’ (F, Ms, Kh, ?H)
 Though there are a couple of odd exceptions, where either expected *β is also vocalized (PU *lämə ‘broth’ > ? *lɛβ > lé : leve- ‘juice’), or *w / *ɣ is not (PU *jekä ‘year’ > ? *ēw / *ēɣ > év).
 Given that PU *toxə- has been considered a loan from PIE *doh₃- ‘id’-, it’s also not clear if this verb ever existed in pre-Samoyedic to begin with. The other widespread PU word for ‘to give’, *a/ëmta-, has also not been attested from Samoyedic or even Ob-Ugric, and it looks likely to be a causative derivative from a simpler root.
 The contrast between Tundra Nenets ā and ă has often been analyzed phonologically as /a/ vs. /ə/, but since TN in fact also has a separate reduced vowel (usually transcribed °), and contrasts long í, ú with short i, u, I consider this analysis untenable; as far as I know, no other language in the world contrasts reduced and unreduced mid central vowels. (In general, the common habit in Uralic linguistics to treat vowel reduction and vowel centralization as separate phenomena seems troublesome to me.) Instead, I would propose simply analyzing ā as long /aː/, and ă as short /a/. The fact that ā comes from earlier full *a, and ă from earlier reduced *ə, should not be considered relevant; especially since ° is historically largely derived from PSmy *ə just as well, and since *ə is regularly reflected as a plain full vowel /a/ also in the Southern Samoyedic languages.