Visible crew/equipment: When Roger and Eddie get in a truck and there's no key, Roger hears the voice of Benny the Cab in the back of the truck. He then slides through a little window and his love letter to Jessica pops out of his pocket. A black glove can be seen pushing this letter through the window.
Continuity mistake: When Eddie Valiant is in his office, and he examines the newspaper photo of Jessica Rabbit and Marvin Acme, the picture doesn't match the photos shown to RK Maroon earlier in the film, and neither does the original of the photo he looks at next. The photo shows an earlier, less sultry version of Jessica, in a halter-neck dress. (Jessica wears a strapless dress throughout the film). The DVD's Toontown Confidential special feature mentions that Jessica's look changed during filming, and the scene where Eddie takes down the Jessica photos and looks at the holiday photos of him and his brother was re-shot to show the new Jessica. Looks like they either missed the newspaper scene or felt that the view was so brief it wasn't necessary to change it.
Revealing mistake: Close to the film's climax, when Doom is showing off his Dip Machine, we see one of the weasels hoisting a canister of Dip up a ladder. If you look close, you can see a large wire pulling the canister up. This was seen in the VHS version and may have been corrected in the DVD, I am unsure.
Deliberate mistake: The window blind in Maroon's office changes to a sheet of tambour (as found in roll-top desks) just before Roger crashes through it. This was to ensure his outline remains perfectly in it, otherwise pieces would drop out which are not attached to the strings on either side.
Continuity mistake: In Valiant' office notice the whiskey bottle to the right of Valiant. Then Roger is about to sit in his brother's chair. While Valiant is yelling at him, look right in front of him the whiskey bottle is there, but then when he sits down the bottle is back at its original spot.