Just after Natalie removes the flower from Monk's lapel, it is in her hand. In the next shot, the top of the flower is clearly visible. After the next change of POV, it's missing again.
Monk and a bar customer take 2 flash photos without rotating the flash cube. A flash cube had 4 single-use bulbs, one on each side. After a bulb was used it was burned out and not reusable. Some cameras automatically turned the cube when the film was advanced; some required the user to turn the cube by hand. Neither happened; the cube was not turned.
During the bar scene, as soon as the bartender walks away, when the camera switches angles, Natalie's left hand has gone from being on her chin to being on the counter, far too fast for it to have moved there on its own.
After Monk and Natalie leave Brody's house for the second time, Mrs. Brody closes the door and walks into the dining room to pick up an envelope. The sound of her footsteps is not synchronized with her actual footsteps.
Early om, Monk states that 40 years had passed since he was tortured by Roderick Brody. However, later on, when Monk speaks to Roderick in the interrogation room, Roderick asks him why he is bringing up something that happened 30 years ago.