Factual error: In the first match between Fast Eddie and Minnesota Fats towards the beginning of the film, Eddie, right after declaring he would start to win after losing thus far, shoots the one ball into the side pocket by shooting the cue into a striped ball. Sharp eyes will notice that he actually hits THROUGH the cue and strikes the stripe into the one with his stick. While a nice trick, this is an incredibly illegal shot and would never have been allowed.
Continuity mistake: In the scene depicting the first game between Eddie and Fats, having just broken off in the first frame, Eddie chalks his cue with his left hand while his right hand is placed towards the butt of the cue. In the next camera shot however (a split-second afterwards), Eddie is chalking the cue with his right hand with his left hand positioned on the upper half of the cue. As a result, the background scene contains a continuity error also - the man with the striped tie is seen putting a cigarette to his mouth in shot 1 but his cigarette is down by his knee in shot 2.
Bert Gordon: How's your hand?
Fast Eddie: Fine.
Bert Gordon: Good. I'd hate to think I was puttin' my money on a cripple.
Fast Eddie: Hey, whaddaya say somethin' like that for?
Sarah Packard: It's all right, Eddie. I'm sure Mr. Gordon meant no offense. It was a figure of speech.
Bert Gordon: That's right, Miss Packard.
Sarah Packard: And a fact is a fact.
Bert Gordon: Smart girl, Eddie.
Sarah Packard: I love you, Eddie.
Fast Eddie: You know, someday, Sarah, you're gonna settle down... you're gonna marry a college professor and you're gonna write a great book. Maybe about me. Huh? Fast Eddie Felson... hustler.
Sarah Packard: I love you.
Fast Eddie: You need the words?
Sarah Packard: Yes, I need them very much. If you ever say them I'll never let you take them back.