Factual error: In the scene where the FBI agents have taken Giovanni Ribisi in for interrogation, one of the FBI agents says at one point "...and I want the whole C:/ Drive backed up on a floppy.", which is pretty hard to do, if not impossible, unless you've got about a 5Mb hard disk drive (depending on compression levels). But later on in the scene where Ribisi is actually doing it, he does it in about 10 seconds...with a 1.44MB floppy.
Other mistake: In the scenes after Giovanni Ribisi is arrested, his looks are constantly changing. In scenes where he is talking to Vin Disel his face is very fat. When he walks by Abby's desk he is thin again. If you get Boiler Room on DVD you'll see an original ending where Ribisi is thin all the way through the end of the movie; Because Giovanni was preparing for a film that required him to gain 30 something pounds, the scenes that needed to be reshot for a different ending are very defined.
Continuity mistake: When Seth's father calls him asking if he can help out with Seth's stock deal, listen carefully to everything said. When the FBI agent plays it back, right before Seth's father leaves the FBI office, saying "You can't charge me with anything," the agent plays back the recording of him and Seth talking, and the placement of what they are saying is totally different from the actual conversation.
Continuity mistake: In the final scene, Seth's Volvo is parked correctly in the parking spot next to a red Ferrari and a grey car. But when the wide shot reveals the FBI vehicles moving in, the Volvo is parked sideways and the grey car is gone. There is no way he would have time to park it like this, and make the other cars disappear.
Other mistake: In the scene where all the guys are in a bar and Greg is about to leave with Seth, a big guy bumps into Greg. When Richie is beating this big guy up outside the bar in the alleyway, you can see that the guy is fully conscious but is letting his arms just lay on the ground without even trying to protect himself. Really bad acting/directing.
Continuity mistake: In the scene where Seth goes into the office at night to get his briefcase/bag after he gets dropped off at his car, he sees the compliance officer shredding documents. The compliance officer's sleeves go from being buttoned at the wrist to being rolled up between shots. There is not enough time between the scenes for him to do this.