At the beginning of the show when Barney shows the IMF group the diamond studded crown, it looks nothing like the one he replaces in the jewel room.
The jewel room floor is rigged with a pressure sensitive alarm, yet Barney walks on it without setting off the alarm.
Barney gets into the treasure room by cutting a square out of the floor. When he leaves he replaces the square by placing a jack under it. However, the final shot of the room shows the top of the square is protruding almost an inch above the floor, making it instantly noticeable.
As Paris is making is descent from Francesca's bedroom balcony via some sort of trellis, his foot breaks one of slats and the noise alerts a palace guard. As Paris is dangling, the guard is practically right below him. It seems odd that the guard failed to completely scan the vicinity.
When Barney is sawing the jewel room floor from below he should be wearing safety eye wear to protect his eyes from all of the falling sawdust.
When Barney removes the section of the jewel room floor, he tosses it off to the side with one hand showing that it very light and not made of heavy solid wood.
While Barney saws into the treasure room after Lucifer (the falcon) sets off the alarm, the alarm bell is briefly shown, but the strikes do not match the sound.
There is absolutely no chance that someone standing on a square of the floor that had been cut out and being held by someone having it propped up with just their shoulders (causing it to shift almost constantly) would not notice the floor moving under their feet. Furthermore, when same said person moves to get out of the way of the falcon, they momentarily put all of their weight onto their left foot (the one on the cut out square), which would have doubled the weight on Barney's shoulders and caused the already shifty square to collapse or, at the very least, cause the guard to stumble over the loss of stability.