If this has been asked before , i apoligize. But how did the circles on the movie prove Kay Fresstone was the murderer ? Any help is appreciated.

I'll try my best to explain this. In the projector booth, Kay turned the timer dial so it would appear that a reel change was coming up and then asked Walter to go get the screen tests. This would give Kay an alibi of being in the booth to make the change-over. However, when Walter came back, he saw the cue blips at the point that "The Professional" shoots himself. At that time, it probably didn't click in Walter's mind that , "Hey, if she made the reel change earlier, those blips shouldn't be there." Also, he was more disturbed by the shooting in the film than he was by seeing the blips. He mentioned the night's timeline to Columbo while Columbo was in the booth, including the fact that he saw the gore in the film just as he returned to the booth and even confirms Kay's alibi. Afterall, if she wasn't in the booth, who made the reel change? Columbo later gets a lesson on the blips right before he interrupts a screening of an old film. We all know, little things tend to rumble around in Columbo's mind until he needs them. As he is sitting in the TV repair shop, "The Professional" just happens to be on at the exact moment that Walter walked in on. Columbo sees the blips, puts two and two together, and realises that the change-over happened later than Kay said it did, thereby giving her alibi a doubt and giving her the opportunity to have shot and killed Mark.

I never got the impression that Walter actually noticed the cue blips. I always thought that Walter just commented on the depraved state of entertainment and how he saw a man blow his brains out right after he returned to the projection booth. When Columbo noticed that the suicide scene had a cue blip preceding it, that meant that Walter was lied to about the timing of the reel change, i.e. that it was much later than Kay had told him, giving her opportunity to commit the murder.

Plus, there was no nickel on the floor proving that....whoops. I’m getting my episodes mixed up, lol.