Just saw the movie as well, and I thought it was awesome. The first person cam style didn't bother me at all, which seems to be what 90% of the complaints towards this movie are based on. I actually enjoyed that aspect a lot because I felt as if it connected you to the movie more so than a typical still cam 3rd person perspective.
For the other 10%...you are expecting a movie that is 100% realistic. You need to remember you are watching a movie. It's a monster film. You don't need to be rationalizing and trying to ponder every little thing that happens. Take it as it goes, and enjoy it.
Edit:
BTW, I also had a the misfortune of seeing the Blair Witch Project. If you have any reservations just simply because this movie has the same first person cam style as BWP, don't worry. It's far from the colossal failure/crapfest that was BWP.
Edit2:
I've got a Sony Handicam that can record for 160 minutes off the battery with NightVision and the LCD view finder turned on, so I don't see why a battery can't hold up for 70 minutes in the movie. I'd like to know what camera it was too, because apparently the bastard is indestructible