Though I often enough blog here about issues of consonantism too, it is clear that the largest challenges remaining in Uralic historical phonology concern vocalism.
Our current standard model of Uralic vowel history is mainly rooted in Samic, Finnic, and Mordvinic (the West Uralic group) on one hand, Samoyedic on the other. The evidence of these languages allows sketching a “canonical” system of eight stressed vowels in the 1st syllable, vs. a two-way contrast in the 2nd syllable. The later development in the other languages has also been surveyed in good enough detail to tell that the system probably is not going to need any fundamental uprooting. Perhaps we’ll eventually end up adding some further unstressed vowels; perhaps we can identify a ninth stressed vowel phoneme. But at least the former kind of updates will probably end up being based on these same key languages all the same.  Unstressed vowels are almost always lost in Permic, Hungarian, Mansi and Khanty, so positing new ones without any direct evidence would be quite questionable.
Mari is however a curious intermediate case. The original trochaic *CV(C)CV stem structure of Proto-Uralic is still partly preserved, though in a more reduced shape than in Mordvinic. But the development of stem vowels seems to diverge according to their parts of speech.
Verb roots in Mari are vocalic without exception, dividing into two stem classes: e-verbs (e.g. *ĭle- ‘to live’, *kånde- ‘to carry’, *pĭšte- ‘to put’) and a/ä-verbs (e.g. *kola- ‘to hear’, *lektä- ‘to leave’, *nelä- ‘to swallow’, *tola- ‘to come’). This distinction quite neatly corresponds to the West Uralic distinction between *a-verbs and *ə-verbs (cf. e.g. the Finnish cognates of the abov verbs: elä-, kanta–, pistä-; kuule-, lähte-, niele-, tule-). There are still a number of exceptions; for many of them I could outline some lines of explanation, but in any case they don’t seem to rock the big picture.
As Mari /e/ in initial syllables regularly reflects PU *ä, it seems necessary to assume that inherited open stem vowels first merged as *ä, and were regularly raised after this. This would be quite similar to Samic, where the distinction between *ä and *a was similarly lost in the 2nd syllable, and the merged sound was in neutral environments eventually raised to *-ē.
The lowering of *ə to *a/*ä is not as trivial to understand, as Mari *a and *ä in initial syllables have no regular origin. Perhaps this is an additional piece of evidence that PU *ə was indeed a vowel quality that did not occur in the 1st syllable? The shift *[ə] > *a / *ä would be itself simple enough.
Nominal roots (including besides nouns also adjectival and numeral roots) are a different story. Almost no full-vowel-stem nominals occur in Mari, recent loanwords aside. The main types are instead consonantal and *ə-stems. Both types show only a simple reduced vowel /ə/ between the root and inflectional suffixes. In the latter stem type, this remains in the nominative; and is written е, ӧ, о in the orthography of Meadow Mari, though unlike actual /e ö o/ it remains unstressed. 
Vexingly, this distinction does not appear to correlate at all to the *a : *ə distinction recoverable from the West Uralic material. And unlike Mordvinic (where a class of consonant stems has emerged by loss of *-ə after single consonants and velar + sibilant clusters), the consonant environment does not seem to explain the duality, either. Final vowels can be either lost or retained after both heavy and light syllables; and this does not change if we look at the situation in Proto-Mari rather than Proto-Uralic. This adds up to a full set of no fewer than 12 different stem type correspondences between Mari and standard-issue Proto-Uralic:
- Light *a-nominal to vocalic stem:
e.g. *kota > *kuðə ‘house’, *muna > *mŭnə ‘egg’, *śečä > *čü̆čə ‘uncle’
- Light *ə-nominal to vocalic stem:
e.g. *kaśə > *kužə ‘long’, *ńëlə > *nülə ‘arrow’, *sülə > *šü̆lə ‘fathom’
- Heavy *a-nominal to light vocalic stem:
e.g. *aška > *ošə ‘white’, *mërja > *mürə ‘berry’, *tälwä > *telə ‘winter’
- Heavy *a-nominal to heavy vocalic stem:
e.g. *külmä > *kĭlmə ‘frozen’, *sonta > *šondə ‘dung’, *täštä > *tištə ‘sign’
- Heavy *ə-nominal to light vocalic stem:
e.g. *ëppə > *owə ‘father-in-law’, *këččə > *kåčə ‘bitter’, *läwlə > *lelə ‘heavy’, *tammə > *tumə ‘oak’
- Heavy *ə-nominal to heavy vocalic stem:
e.g. *oŋkə > *oŋgə ‘fishing hook’, *kośkə > *kåškə ‘rapids’, *wartə > *wŭrðə ‘shaft’
- Light *a-nominal to consonant stem:
e.g. *ora > *ur ‘squirrel’, *kala > *kol ‘fish’, *pata > *påt ‘pot’
- Light *ə-nominal to consonant stem:
e.g. *kätə > *kit ‘hand’, *lomə > *lŭm ‘snow’, *sënə > *šün ‘sinew’, *werə > *wü̆r ‘blood’, *wetə > *wü̆t ‘water’
- Heavy *a-nominal to light consonant stem:
e.g. *ojwa > *wuj ‘head’, *jalka > *jål ‘foot’, *neljä > *nĭl ‘4’
- Heavy *a-nominal to heavy consonant stem:
e.g. *oksa > *ukš ‘branch’, *lupsa > *lŭpš ‘dew’, *mëksa > *mokš ‘liver’
- Heavy *ə-nominal to light consonant stem:
e.g. *ëptə > *üp ‘hair’, *künčə > *kü̆č ‘nail’, *pučkə > *pŭč ‘hollow stem, tube’, *śarwə > *šur ‘horn’
- Heavy *ə-nominal to heavy consonant stem:
e.g. *mekšə > *mükš ‘bee’, *soksə > *šukš ‘worm’
I get the feeling that this mess cannot (and shouldn’t) be resolved starting from just the canonical PU root structure and designing sound changes fine-tuned for exact vowel and consonant environments. E.g. supposing that *ə remains after *l, as in ‘arrow’ and ‘fathom’, will make it difficult to explain the consonant stem in ‘fish’. Probably at least one stem type distinction has been retained here that does not systematically survive in West Uralic.
This doesn’t mean that there couldn’t still be minor conditional sound laws involved, of course; e.g. heavy consonant stems seem to involve only plosive + *š clusters, and probably a similar conditional loss of *ə has occured here as did in Mordvinic. (Altho there are still words like *kukšə ‘dry’, *upšə ‘hat’ to be found as well.)
On the other hand: the fact that only nominals are this much of a mess suggests another avenue of explanation. Probably some parts of the situation can be cleaned up by distinguishing inherited and loanwords. Loans are typically nominals, and this can easily lead to a larger number or proportion of unetymological root shapes appearing in them. Consider e.g. Baltic *kerta → Finnish kerta, Mordvinic *kirda ‘time, instance’. If we naively equated the distribution of this word with its age, we might end up reconstructing a common West Uralic proto-form *kertä. But the expected reflexes of this should rather be *ä/*ə-stem forms: ˣkertä, **kiŕďə.
Verbs by contrast are somewhat less likely to be loaned. Modern Finnish makes a particularly striking example: in underived verb roots the etymological vowel combinations /e-ä/, /i-ä/ remain still more numerous than the loanword combinations /e-a/, /i-a/, although in nominals the battle has been lost ages ago (perhaps already in Proto-Finnic).
My next step in untangling this issue would probably be to tabulate how 1) widespread Uralic roots, 2) areal possibly-Uralic roots, and 3) known loanwords of various age are distributed in Mari between the 12 classes. Preliminarily, it seems that at least type #2 (*CVCə > *CVCə) is numerically much overshadowed by type #8 (*CVCə > *CVC). And here at least *nülə could be suspected of being a family-internal loanword from some direction, since this actually has an unexpectedly specific sense ‘arrowhead made of bone’, while the neutral Mari word for ‘arrow’ is instead *pikš. It would have to be a very old loan though, since it shows the expected proto-Mari sound changes *ń- > *n-, *ë-ə > *ü, *ü > *[ö] / _R. 
Additionally, a second bisyllabic nominal stem type might have to be set up for Proto-Mari, for words where Hill Mari has a consonant stem but Meadow Mari has a vowel stem. It does not seem immediately clear if this correspondence can be always derived from an original vowel stem by apocope. Examples of this correspondence among the words mentioned above include ‘fathom’ (-lə₂), ‘berry’ (-rə₂), ‘oak’ (-mə₂) and ‘hat’ (-pšə₂); but not ‘house’ (-ðə₁), ‘egg’ (-nə₁), ‘uncle’ (-čə₁), ‘father-in-law’ (-wə₁), ‘bitter’ (-čə₁), ‘long’ (-žə₁), ‘dry’ (-kšə₁). This could add some extra resolution as well.
Finally, I’ll note that Mari also allows monosyllabic nominal stems. These regularly reflect roots with earlier medial semivowels or spirants, regardless of the original stem type: e.g. *kiwə > *kü ‘stone’, *luka > *luɣa > *lu ’10’, *śüd₁ə > *šü ‘coal’, *täjə > *ti ‘louse’.  But, interestingly, and further highlighting the stark split in stem type behavior between verbal and nominal roots in Mari, there are no monosyllabic verbs to go along with these. Candidates for monosyllabicity end up as bisyllabic CV.V stems instead, again with exactly the expected stem vowel. E.g. *jëxə- > *jü.ä- ‘to drink’, *kajwa- > *ko.e- ‘to dig’. Does this perhaps indicate that monosyllabic nouns should be considered a subtype of consonant-stem nouns, even though no nominals of a shape **CVə seem to occur?
 A few good candidates are indeed already provided by two kinship terms:
– PS *nōtōj ‘husband’s sister’ ~ PF *nato ‘spouse’s sister’ ~ PSmy *nåto ‘spouse’s younger sibling’
– PS *kālōj ‘husband’s brother’s wife’ ~ PF *kälü ‘(husband’s) brother’s wife’ ~ PSmy *kälü ‘sister’s husband’
The argument for reconstructing a “kinship suffix” *-w for these (*nataw, *käläw?) appears to be circularly motivated by the belief that PU did not allow any 2nd syllable labial vowels. On the other hand, the unstressed labial vowels in Proto-Samoyedic are a relatively new discovery as well, and before that, words like these could have well been counted among the words that have innovated 2nd syllable labial vowels in Proto-Finnic and Proto-Samic. — On the third hand, I also wonder if the problematic sound correspondences in a third similar word: PS *vivë ~ PF *vävvü ~ PSmy *weŋü ‘son-in-law’ should be attempted to resolve by constructing something like PU #weŋäwə, with Samic *-vë not corresponding to PF *-vvü and PSmy *-ŋü, but instead only to their final labial vowel.
 I have seen phonological descriptions of Meadow Mari that attempt to follow the orthography and identify final unstressed -е, -ӧ, -о with /e, ö, o/ (e.g. Eeva Kangasmaa-Minn’s description of Mari in the 1998 reference book Uralic Languages by Routledge), but this seems like a terrible idea to me: it clashes with regular stress assignment on the rightmost full vowel, and requires setting up a rule by which final /ə/ becomes one of the full mid vowels, depending on vowel harmony. I sort wonder if the analysis lingers out of some kind of attachment to vowel harmony? which this schwa-fortition rule would be the only example of in Meadow Mari.
 Another option might be to assume that the final vowel represents some kind of a fossilized derivational element.
 It also appears to be the case that just about all of these cases have close tense vowels *i, *ü, *u.