Not as far as I can tell. Is there some dodgy dialogue? Sure. But much of it's fine. I actually like the characters, which I think is of great importance. The voice acting, in my opinion, is as good as the previous games.
As regards Star Trek games or, rather, games offering a Star Trek-like experience: all the ones mentioned so far don't really scratch the itch that I am -- and I assume also @divedivedive is -- looking for. And that's a game that gives freedom when it comes to exploring the galaxy and also offers a decent story (missions!) with memorable characters. Star Control is not a bad suggestion, but it doesn't come close to the kind of detail offered by Mass Effect (or something like Star Trek: 25th Anniversary or A Final Unity). It really should be more along the lines of an adventure game and/or an RPG.
And as far as actual Star Trek games are concerned: Bridge Commander and stuff like Tactical Assault come close, but don't allow you to actually land on a planet and run around there; they stick quite close to being arcade-like space simulations. That's also the reason why something like Elite: Dangerous doesn't fit -- too much flying around, space combat, and trade, and not enough exploration, meeting new aliens, plot. Similarly, No Man's Sky does the flying around and exploring strange new worlds, but has no story or engaging characters. Star Trek Online seems like it would fit the bill, but it does nothing for me -- it's far too much of an MMO than anything else.
So Mass Effect it is. And that's definitely not a bad thing.
Edit: as far as the facial animations, I remember the "dead eyes" stare in BioWare games has been a running joke in Zero Punctuation reviews of their games for as long as I can remember. Strange that it's largely gone unmentioned by most other people until Andromeda. That's not an excuse, of course...