Trivia: After Thomas has stolen the first painting and is coming out of the museum main gates, you can see a balcony in the background with a man in a bowler hat and suit standing on it. A clue to viewers who notice it maybe?
Trivia: Not strictly a mistake, but have you ever seen anything like the product placement when Rene Russo storms into an office and downs a can of Pepsi One (with the label cunning facing the camera)? She does all but turn to camera, hold it up, and say "aaah - there's nothing like an ice-cold can of Pepsi". I actually laughed when I saw it.
Trivia: In the ball scene when Pierce Brosnan dances with Rene Russo you will notice that Pierce Brosnan's tie is never tied. It was part of his contract as being James Bond that he not wear a full tuxedo in any other movie.
Trivia: Not a mistake, just to notice: Thomas Crown (Pierce Brosnan) uses the name Jimmy more than once. First, he refers to his chauffeur by that name; next as he walks into his office, he calls out to another employee by that name; later in the film, even a security guard is called Jimmy. [Maybe a bit of observation; it used to be not uncommon for Glaswegians to call everyone 'Jimmy'.]
Trivia: The car that Crown drives on Martinique was originally intended to be used for Arnold Schwarzenegger's character in Last Action Hero, another John McTiernan film.
Trivia: The large delivery truck that almost hits Thomas Crown at the very beginning, as he walks across the street to the museum, is actually the same truck that is carrying his "Trojan horse" to the museum. The driver and license plate are the same (PB9975). In line with the theme and use of the Greek "Trojan Horse" is also the idea of a Greek tragedy; that he (Crown) would be killed by the very truck he hired to carry out his heist; felled by the very events he put into motion. An important part of Greek tragedy is hubris which is shown prominently in Thomas Crown. (00:02:45 - 00:05:10)
Trivia: The actual glider used in the movie was a "Duo-Discus x" manufactured by Schempp-hirth and was the personal plane of millionaire Richard S. DuPont. The gliders sold new in 1999 (when the movie was made) for about $100,000. The DuPonts, besides being chemical giants, were pioneers in American gliding. (01:06:00)
Trivia: In the 1968 version of this film Faye Dunaway plays the major role of the insurance lady. In this version, 1999, Faye Dunaway plays the role of the shrink for Mr. Crown.
Trivia: The dress that Rene Russo wears that is transparent in the dance scene actually belonged to the actress that played Thomas Crown's protege Anna. She wore it to the set on a lark and the directors liked it so much they put it in the movie.
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.