Continuity mistake: At the very start of the show, Frasier is pretending to conduct an orchestra with a wooden spoon. Marty says "Boo," and we see the spoon in his right hand. Then Ronee says, "He does scream like a woman," and suddenly the spoon changes to his left hand and is turned the other way. Frasier had no time to change it.
Continuity mistake: At the hospital the nurse comes over to talk to Frasier about his father - her paper on her clipboard is flipped over the back of it and her hand is holding the side of it. A couple of shots later, with no opportunity to change positions, the paper is no longer flipped over and her hand is lying on top of the clipboard.