Continuity mistake: In the end when the Kothoga is on fire and chasing Margo, it catches up to her in moments. However, everytime it dramatically changes angles, the Kothoga appears alot futher away than it was previously, but soon after catching up once again. Noting her progress in the room, this situation is NOT simply replaying the same scene from different angles. Plus when she gets to the water tank, she has plenty of time to spare to hit a lever, climb the device, and jump in before the Kothoga looms overhead.
Plot hole: What happened to the two boys who stayed in the museum past closing, after the homeless guy seemed to attack (or at least be seen to be stalking) them? The next time we see them, it's the next morning, and they're fine. So where did they go? Who helped them? What happened to the homeless guy? The boys couldn't have just hidden, as the homeless guy has been in the museum for ages, and these two boys just got there that day. The homeless guy would have known all the nooks and crannies and every little hiding spot available; he would have caught them.
Continuity mistake: When the two police dogs, Castor and Pollux, run into the dark tunnels and away from the policemen, one of them, Castor, winds up being killed by the Kothoga. The officer who cared for them, Bradley, goes chasing after Pollux in the dark with his flashlight, and Lieutenant D'Agosta chases after him, with a flashlight of his own. After Bradley finds Pollux, he's talking to him and still using his flashlight, when he gets killed by the Kothoga. However, after D'Agosta gets into that room, there is no flashlight lying on the ground, let alone shining on Pollux - as it fell only moments before.
Deliberate mistake: When Margo is in the Superstition exhibit, she thinks she hears/sees something and runs for her life. She gets into the women's bathroom and tries catching her breath before the mirror. Hearing a noise outside of the bathroom, she goes into a stall, locks the door, and stands up on the toilet so her feet don't touch the floor. It was just a little old maid washing her hands outside the stall, and the strange sound Margo heard was the maid using her inhaler. However, how is this little old lady - with asthma, we can assume - supposed to have gotten all the way from deep inside the exhibit to the women's room within seconds, pushing a big heavy cart? Why would she even be in such a hurry? We can assume, however, that perhaps this was a deliberate mistake to show that, after all, maybe Margo wasn't just freaking out over nothing...that perhaps something was in the exhibit with her.
Factual error: In the book by Douglas Preston and Lincoln Child, the monster has been in the museum's subbasement for around seven years, making the lair filled with either partially or fully decomposed skeletons completely plausible. However, in the movie they change the duration to only six weeks. The lair they find in the movie with tons of skeletons doesn't connect with the time it took for them to become that decomposed.