Shortly after his patient's suicide, we see Bill from behind talking with an another man, and he makes some comment about suicide and motions to his head with his right hand. But when the camera shows him from the front, he is putting his left arm down.
In the first car chase, as the red car slams into the rear fender of Capa's car we see, in close-up, the front end of the red car smashed in. In the next wide shot of both cars, the front is completely intact, with no damage visible.
During the first car chase, the passenger's side of the red car slams into a truck while the driver's side is shown unscratched. In the following close-up shot of the car, the driver's side is show severely damaged. But in the next shot the damage is gone.
The goof items below may give away important plot points.
Rose pulls out all the stops when disguising herself as "Richie," and thus looks fairly different in drag. Besides a short blonde wig and Coke-bottle glasses, the Richie getup also appears to include green contacts, as well as what appears to be facial prosthetics, pale lip color (to make the lips appear less full and less feminine) and fake eyebrows. During the big reveal in which Bill removes Richie's glasses and blonde hair, the contacts, eyebrows and prosthetics are all conveniently missing in the final shot of "Richie" (possibly to make Rose's de-transformation in the film quicker), although we don't see Bill remove any of those things in the previous shot, in which the entire disguise is still intact.
It's highly unlikely that Mrs. Niedelmeyer would know that Richie hanged himself since Dale buried the body and Rose assumed his identity. This is corroborated by the fact that Rose is going to therapy as Richie.