I think a lot of people make valid points about issues that are likely with a lot of MILs, but I think that maybe a couple that have been touched on are the most basic/inescapable. First, the fact that the two of you are in a close and (theoretically, of course) permanent relationship without having chosen each other or even formed each other in any way, and second, the inculturated (and probably accurate) feeling that on some level, they're always judging you and your adequacy as, essentially, their replacement.
Once we're adults, generally speaking there's no real reason for us to form a lasting, close relationship with someone that we're not fairly compatible with--except this one. I say lasting and close because I think those both matter a lot--if the relationship were going to be temporary, we wouldn't care nearly as much--and if it weren't supposed to be close ("mother", for goodness sake), we probably also wouldn't care. If/when there are other people in my life--casual friends, neighbors, whatever--who are sufficiently different from me that we have to stay on the level of civility, then no one really cares. That's fine and to be expected. But with my MIL I always regret that we can't find our way to be closer, because dang it, we're family. But we don't choose our in-laws, and there's no guarantee whatsoever that we'll have anything in common or compatible belief systems. My MIL is a saint of a MIL and grandma and a woman I can find plenty of reason to respect on a lot of levels, but we differ on too many fundamentals and I try to be accepting of the fact that ultimately, we'll never be "friends", just basically civil. And there's no interaction between our differences, though I can't express this part well. I differ from my mother on a lot of points, too, of course, some pretty basic, but I know what they are and I know how to just avoid them, without much extra effort on my part, because she raised me. With my MIL, both of us are constantly walking on eggshells in an effort to not offend, and basically every time we're together, I have an amusing story of how I failed and almost certainly shocked my poor MIL with some statement or action or another to tell my husband when he gets home. It's funny then, but it's also TIRING. I think that actually all the same things irritate both my husband and I about both of our mothers, but, well, my mother is my mother, fundamentally, and his is his. (Though you'll forgive me for being grateful that his mother figured out well before me that her son was very little like her and that she'd never really understand him and was big enough to just accept him.)
The second thing I mentioned is the "judging her replacement" thing, which as far as I can tell is perfectly valid. My MIL never says anything direct, never criticizes, not even passive-agressively, but sometimes the tongue-biting itself is palpable, you know? I KNOW she thinks I'm not a very good housekeeper (which is valid enough on the one hand, and a good example of how biological and legal relationship is different. My mother can understand that my standards differ radically from my reality because my health and energy levels are never what they should be, but to a MIL who hasn't seen these health problems up close, that's going to sound like an excuse at best). She probably has problems with my parenting too. Why wouldn't she? I would, in her position. We disagree, and while we can avoid it in conversation, it's gonna be obvious enough in practice. Of course that's going to annoy her!
Those two points, for us, add up to a fairly tense relationship without need for any greater dysfunction, and those two dynamics are going to exist, I would think, in all but the luckiest of MIL-DIL relationships. I wish it were otherwise. My MIL drives up once a week (from an hour away) to help with Evelyn and around the house, and every time it's a mix of anticipation of the help and dread of the eggshell-walking for me. Sigh.