All over the internet it seems that much of the criticism of Mass Effect: Andromeda seems to fixate on the poor facial animations. Are the animations poor? Yes, they are, and I think even animators at BioWare would agree with that. I do think the amount of criticism is excessive and I think the fixation on it makes it tough to find and honest review, but I don't think it's unfair. Mass Effect has long been known for its storytelling, and when the faces of those telling the story aren't convincing, it really harms the ability of players getting into the storyline.
I do think that a shortcoming of this magnitude is inexcusable. While some animators have said that it is because of improved graphics and players becoming more adept at seeing poor facial animation, I do not think this is the case. While the lips weren't always perfectly synced in previous entries, for the most part the eyes were believable (i.e. looking in the correct direction, having proper glossiness, blinking as is appropriate, etc.) and the mouths weren't doing motions that humans simple can't or don't do. If you don't believe me, I'd ask that you go back and watch a few cutscenes from Mass Effect 3. While far from perfect, the facial animation is far less distracting.
In a time where facial capture has been in use for over two decades (for example, it was used heavily in animating Gollum's character in Lord of the Rings), it seems that animation this poor should be well in the past. I would hypothesize that much of the facial animation was not actually done by animators, but rather by software, the animation is far too poor to have been done by someone who has actually watched someone speak.
So, what should be done about this? Unfortunately, I don't know that there is much that can be done, at least not reasonably. The best solution would be to bring everyone who voices a human or asari back in and record their lines again with facial capture (this would also help cure some of the really inconsistent/poor voice acting that comes up in places) and replace the current animations. Unfortunately, this is likely not feasible. Another option would be to use video footage and track the lips and other points on the face to try to get a profile for animators to go off of. Either way, a lot of time would have to be invested to fix the facial animation problem.