Pretty much all of the dialog between Martin Lawrence and Will Smith was ad-libbed. The original script can be found here: http://www.imsdb.com/scripts/Bad-Boys.html, as Don Simpson and Jerry Buckheimer thought it would be better and more funny. See more...
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Continuity: When the two female characters enter the fancy hotel room, they make a point to say they will only be there for a couple of minutes. It is daylight when they go in. The visit is cut short (the one that's supposed to be a few minutes long) because of a gun battle in which one of the women dies and the other escapes. The escaped one gets out through the roof into an evening's sky. There's still light visible, but for a visit that lasts all of 4 minutes, it's far too quick a change.
Continuity: When Marcus meets Julie Mott she attacks him with a bat. He takes the bat off her and moves to leave. The next shot of Julie Mott sitting on the floor shows the bat in the foreground. Cut back to Marcus still holding the bat and he asks her, "Look lady, you ain't got no more bats, do you?"
Continuity: When Marcus is talking to his wife in bed about having some early morning sex, she gets up and he is leaning on his side. She tells him the kids will be coming any minute and when they do come bursting through the door, Marcus is now under the covers on his back. Given that we heard them approaching, there's no time for him to move.
Continuity: When Marcus and his wife walk up the stairs in the house, they are having a heated discussion and his wife (off camera) shouts down "and you don't even have your wedding ring on." At this point his wedding ring IS on his finger, then in the next shot the ring is NOT on his finger and Marcus attempts to put it back on.
Continuity: In the final car chase - in the close-ups - we see Marcus turning the steering wheel quite far from side to side. With the speed they are going that would make the car slalom severely - and probably go out of control. At that speed only very small movements of the steering wheel are necessary (and safe).
Continuity: The kegs of ether in the truck have hazardous material labels applied to them. These are diamond shaped labels that indicate the class of material in the container. Throughout the chase scene they alternate between Flammable Liquid labels (solid red) and Flammable Solid labels (half red, half white).
Other: At the very end of the movie Mike has the bad guy down on the ground and he's got his gun in the guys face, we see a shot looking straight up the gun barrel with Smith's eyes over the top of it. If you look at the barrel of the weapon there is a little point of light at the back of the barrel. This is caused by sunlight shining through the firing pin hole in the back of the chamber showing that the gun has no round in the chamber.
Continuity: In the scene at the beginning of the film, when the villain of the piece shoots Julie's friend, he proceeds to turn the gun on Eddie and shoot him in the leg. After Eddie reels back in pain and falls into the chair, a conversation begins. Throughout the course of this conversation, the drool that flew from Eddie's mouth and landed on his right lapel, disappears and then reappears.