MASSIVE SPOILERS!
I have of complains, but there seem to be glaring physical contradictions:
1. Okay, so it's our future selves doing to our past selves, and in the future we can fold space time blah blah. So if we can do all that, why can't we just send a complete message down to our past selves to tell our past selves ... well, pretty much everything. Either you can communicate or not, and if you can't, fine, but if you can, and you can create wormholes, and control the inside of black holes, and so on, why do you have to communicate at 10 bits per century?!
2. Either the black hole destroys what goes into it, or not. So, we see BOTH a huge lava-flow of the accretion disk, which is presumably mashed and superheated ... everything in the area ... but somehow Coop's ship (not to mention Coop!) manage to ride the wave through the event horizon. If it was just black, that would have made more sense; as was, it was both hell and not hell. And if you want to use "we learned to control blah blah blah", see above.
3. Whereas I completely LOVED the David Bowman homage where Matt Damon blows himself, and the space station to smithereens, I thought that the whole "save" was ridiculous. Maybe you can match the spin of the station, but something with that much inertial could never ever even be stopped by the fine nav jets on the shuttle. It should have torn the air lock right off the top of the shuttle (or v.v.).
4. Why, in whatever future year this is, is everything still being done on Lenovo laptops, fer k's sake!
5. The robots were, not to put too fine a point on it, mechanically ridiculous, not to mention that they (and everything else) had 24x80 green screen on them dumping linux whatnot for no reason at all.
Okay, I wasn't going to complain about high level plot, but I will:
6. If you're thinking of asking M. Night Shyamalan remake 2001...don't! (Yes, I know it was Christopher Nolan, nit MNS, but the stupid "ghost" plot device was so utterly transparent, just like every stupid MNS movie, that I almost laughed aloud in the theater...or perhaps groaned aloud, because they basically gave the plot away in the first five minutes. At least in The Sixth Sense, MNS hides the reveal fairly well. CN just basically wrote "It's your father sending you messages from the future." in giant red (gravitational) letters on the screen! totally ruined the whole thing for me!)
Coincidentally, the surprisingly excellent Edge of Tomorrow just came out in DVD. Highly recommended! Doesn't even try to be accurate (thank god!), but hella fun!