Other mistake: Near the start of the movie when Thomas Crown enters his office for the first time, he uses a magnetic swipe card to access the elevator to his office. After he swipes the card, you can hear a 'ding' and the sound of elevator doors opening but you'll notice as he first inserts the card into the reader that the doors are already open. (00:05:30)
Other mistake: When Catherine breaks into Crown's house, her assistants immediately get to work on the security panel. When the first assistant touches the panel, it falls off the wall and he has to quickly push it back into place.
Other mistake: When Thomas' keys are taken and copied, the name "Medeco" appears on the keys. The duplicating machine used is for standard keys and cannot be used for Medeco keys.
Other mistake: When Catherine breaks into TC's house and is searching for the Monet there is a scene where she admires The Mirror Of Venus, the footage of this scene has been flipped because the painting is a mirror image of it's actual composition.
Answer: I believe that the Monet that Crown hides in his study is not the one that was stolen, it is a copy that he already had prepared. He can enjoy the copy knowing that the original (with the broken spreader bars) is also in his possession. The stolen original then goes to the forger who repairs the broken spreader bars, and then paints another painting (using water soluble paint) over the Monet, so he can "return" it to the museum 3 days later. It gets more complicated when he discovers that Russo is on to him so he has a second forgery made (even the edges forged to match) over the top of "Dogs Playing Poker." He doesn't know if it will be necessary, but given his research into his new adversary, he concocts this contingency. It is likely that he has many contingencies in place, but the "Monet with a ghost underneath" is the only one we get to see. Of course for my theory to hold water, there must be (or have been) that earlier forgery - unless it has been destroyed.
It's not the forgery that he takes out of the briefcase. Even if it were, he still put the Monet in the briefcase at the museum and would have had to break the frame to close the briefcase, thus also breaking the paint and tearing the canvas. The real answer is that it is just something that couldn't really happen, and the movie people don't want the viewer to notice.