Factual error: In the scene where Chris Rock and Anthony Hopkins are driving through the woods with the bomb, they crash head on into a tree. The car they are driving is quite obviously a new model, but the air bags don't deploy. They also crash again when they go over the bank at the end of the field, and again, the air bags don't deploy.
Factual error: In the scene where Chris Rock and Anthony Hopkins meet the Russians in the park to discuss the details of the money/bomb exchange, we see a sniper on a high roof-top. The sniper is several stories up and off to the side of the exchange. But then the view switches to a "sniper's-eye" view through the scope and shows the Russian from straight ahead and at the same level as the scope. This scene is full of errors as the "sniper" is also using an older Russian Dragonov rifle (a good gun for it's time, but hardly the weapon of choice for a cutting-edge CIA agent). He is also standing to take a shot that looks like it is at least 300-400 yards away, instead of laying on the rooftop and bracing his weapon on something.
Factual error: In the montage where the CIA is following Jake playing chess, they show him playing in Washington Square Park, then in Central Park, and then again in Washington Square Park. You can tell this because the Washington Square Park chess tables show the neighboring street and the entrance to the park in the background, while the Central Park chess tables are in the middle of the park, in an area well above the ground level. There is no mention of days elapsing between the change of venue (since they only had "9 days" to find and teach him and 8 days the next day when he was awoken). As for the games, Jake announces "checkmate" and captures the king. A chess hustler who takes on all comers for $20.00 a game wouldn't bother announcing checkmate (or check, as he did in the movie).
Factual error: When Chris Rock plays chess on the street on a chess park table, you can see that the right square on the board is black. Any chess player knows that a board must be set up white on right. Something that makes this mistake even bigger is that Chris Rock is playing chess on a downtown chess table, not a personal board. Meaning the whole table was made wrong by the architect, no way would a city let that kind of error continue. You can also notice that the table Anthony Hopkins is playing on was constructed properly.