Trivia: The entire "How am I funny?" scene was improvised by Joe Pesci and Ray Liotta.
Suggested correction: False. Joe Pesci told the anecdote to Scorsese in the earliest stages of the movie. Scorsese asked him to add it during previous script readings and further rehearsals while notes were being taken by crew members. Then it was finally shot following those rehearsals and notes. In this video all the actors involved tell how Scorsese works and even he himself says he rewrote that scene 4 times. Minute 13:04: https://youtu.be/_bbzUZuxEB8.
I have actually seen interviews where they admitted it was improvised. The reactions from the other actors was genuine.
Just submitted a link to a video where they tell how they improvised during rehearsals and then scripted it.
Revealing mistake: Morrie gets whacked by Tommy with an ice pick. After that, Morrie is dead and lifeless. Soon after, Frankie Carbone (post Jimmy leaving) exits the car. When he does,the car light comes on and you can see Morrie blink. (01:45:40)
Continuity mistake: When Tommy kills Stacks he shoots him once in the back of the dome, then cracks Carbone's castanets about the coffee. Then it cuts to a slo-mo reprise of the whacking with a Henry voice over and Tommy shoots 6 times.
Suggested correction: After Tommy shoots Stacks in the back of the head, you see Carbone come into the room with the coffee pot, a shocked expression on his face. While the camera is focused on Carbone you can hear Tommy continue to shoot Stacks several times off-screen.
Also, the slo-mo of Tommy shooting Stacks the blood splatter is already on the wall before he shoots him.
Continuity mistake: At the beginning of the movie they pull to the side of the road and stab and shoot the not yet dead man in the trunk. In this scene Jimmy shoots him 4 times. Later, when they get to this scene in the story and show it again in slow mo, Jimmy fires the gun 5 times. (01:00:34)
Suggested correction: Jimmy shoots the gun 3 times in each scene.