Plot hole: Property is destroyed, museum windows are crashed through, a giant octopus splashes about in the National Mall's reflecting pool, and even the statue of Honest Abe at the Lincoln Memorial comes alive. With all this occurring, not a single D.C. resident seems to notice and nary a single police officer turns up to investigate the goings-on.
Other mistake: When Larry first enters the main storage room, he has to go by the guard Booth. A voice says "ID" then acknowledges that it's "Brundon, later dude". When it shows Larry from behind it shows a clear shot of the inside of the entire security room. It is completely empty. Did a ghost ask for the ID?
Continuity mistake: In the scene where Larry and Amelia escape into the VJ Day photograph, Larry is seen speaking to a sailor in dress blues. Throughout the exchange the rating badge on the sailor's arm changes from crossed keys, the insignia for storekeeper to lightning bolts, the insignia for radioman several times.
Continuity mistake: In the opening sequence Sacajawea is placed in a crate of tan, straw-like packing material. When Larry visits the museum a few hours later, Sacajawea emerges from a crate full of white packing "peanuts" (styrofoam pellets).
Continuity mistake: When Larry makes the batteries fall out of Brundon's flashlight, they fall all over the floor. During the rest of the scene, as Larry is walking away, there are no batteries on the floor.
Factual error: On the shoulder of the Tuskegee Airmen, their 'American Flag' patch is seen having 50 stars. At the time of WWII, the US flag only had 48, and 48 would have been the number they'd wear.
Continuity mistake: When Ben Stiller is dropped off from the red plane in the middle of the street, the streetlights in the background are yellow for a moment, then switch to another angle and they are green (without adequate time to switch back), then they constantly switch between green and red depending on the camera angle.
Other mistake: In the fight scene between Larry and Kahmunrah, Larry throws the tablet to Amelia Earhart and she opens the gate, but she didn't say the magic words to open it or even worse she doesn't know those words as Kahmunrah.