I found I didn't really know the answer to this question, so I looked it up.
Quote:
from Comparative Greek and Latin Grammar (Andrew Sihler, Oxford 1995)
Final -m remains in L, but there is some uncertainty about what sound was actually pronounced. In poetry it does not interfere with elision when the next word begins with a vowel, but on the other hand it 'makes position', like any other consonant, when the next word begins with a consonant. The letter itself is frequently omitted in early inscriptions (even carefully carved ones). In addition to these facts evident in the texts themselves, there are comments by the ancients. Roman authorities bequeathe to us a special term, mytacism (variously spelled), denoting an objectionable mispronunciation of final -m; and there are stray remarks by Romans, more tantalizing than informative, such as Cicero's statement that 'with us' is nobiscum because cum nobis would be obscene.
The ablest analysis of the question pins down the phonetics of -m as a nasalized [w] in careful speech, which in poetry behaved like a final glide and in casual speech styles seems to have dropped altogether. In certain fossilized phrases the complete loss of m with elision of the preceding vowel was established even in careful speech: animadverto 'notice' (animum adverto) or veneo 'go for sale' (venum eo).
Mytacism, then, seems to denote the mistake of pronouncing -m as an actual [m]; before a vowel, for the Roman ear, such an [m] had to belong to the FOLLOWING word: so partem agis 'you play the part', if pronounced [partemagis], could only be understood as parte magis 'in part rather'.
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So if they're tipsy & casual, I guess they should be omitting final -m. If they're being careful, on the other hand, I guess they should be pronouncing it as a nasalized [w].