When the cat is dropped down for the trial run, it has one green and one blue eye. Later, when Kono finds the cat it has two blue eyes.
When McGarrett first drives up to the museum the entire camera crew is clearly reflected on the side of his car, and when he pulls away they are clearly reflected again.
The theft of the cloak is planned very intricately, and the thieves have 4.5 minutes between the guards' rounds to get in and get out. It would be almost impossible for 2 people to climb down a rope, set up the apparatus, steal the cloak, break down the apparatus and pack it, and climb back up the rope. In fact, as done in this show, it takes 8.5 minutes, so assuming the guards are not asleep, the thieves should have been caught in the act.