Continuity mistake: In the scene outside the hospital, when Gale and Sidney try to make the protagonist reconsider her plan to leave, Courteney Cox's hair changes position in front of either shoulder several times between shots.
Continuity mistake: When Sam is assaulted at the hospital the first time, Ghostface misses Sam with his knife, which gets stuck on a poster on the board. By mistake, he 'stabbed' the third column of the text on the poster, but then the knife is stuck in the first column instead, then he pulls him out from the third column again, resulting in a hole in the second column. (00:23:55)
Continuity mistake: The first time we see Sam, it's in a long shot as she is sitting outside the bowling alley in Modesto. Look at the shadows on the building, in particular the door Jack Quaid comes out of; they change between shots.
Continuity mistake: After Ritchie gets stabbed through the cheeks, as Sam mounts him and begins stabbing him, his cheek wounds are missing in a few of the wide shots.
Continuity mistake: When Sam stops and sees her father reflected in the cop-car window at the end of the movie, in the shots focused on Sam, police lights are reflecting off her entire face, but in the shots focused on the reflection in the window, they're only reflecting off one side of her face.
Continuity mistake: After Sam stops stabbing Ritchie, the amount and pattern of the blood on her face and shirt changes between shots before she slits his throat. Then, when she stands up a few shots later, the amount and pattern of the blood changes again completely.
Continuity mistake: After Gale screams, "You killed my best friend!" and Amber replies, "He died like a pussy!", they get into a tussle. Gale punches Amber, making a blood smear appear on her chin. The blood smear is instantly missing in the next shot, and then reappears a few shots later.
Continuity mistake: When Ritchie and Sam fall down the stairs, Ritchie goes from being face down on the ground to suddenly being semi-lifted up and reaching for the gun instantly between shots.
Continuity mistake: When Amber mentions that she met Ritchie on the "Stab" subreddit, Ritchie goes from having his gun pointed at Sam's chin to up and pointed at her face between cuts.
Continuity mistake: When Ritchie is revealed to be the killer, he pulls out the voice-changer to taunt Sam. However, after he says his line, it completely vanishes in the next shot.
Continuity mistake: When Sidney and Ghostface go over the railing, the way they land on the ground (face up, feet towards the railing) doesn't line up with how we see them fall. They should have landed face up in the opposite direction.
Continuity mistake: When Sidney and Gale see Amber come out of the house screaming, Sidney asks Gale, "What do you think?" Gale starts to turn her head towards Sidney, but midway through, it cuts, and she's suddenly looking forward again.
Continuity mistake: When Mindy is oblivious to Ghostface behind her, watch Ghostface's hands. In one shot, he lifts his left hand up near his cheek, but it's not there in the next shot. Then he starts to lift his knife with his right hand only, but in the next shot he's holding it with both hands, and it's moved from his side to in front of him.
Continuity mistake: When Liv is angry and talking to Mindy about how she might be the killer, Mindy's position on the couch changes repeatedly as it cuts between her and Liv. You can use the gap in the padding behind her as a reference. She keeps moving back-and-forth about 1'.
Continuity mistake: When Ritchie breaks up the party and makes everyone leave, the people walking towards/through the doorway are different from shot to shot, and sometimes the same people walk by twice. For example, the same guy in a denim jacket and yellow shirt walks by Ritchie twice. A black girl is about to walk by Ritchie in one shot but is missing from the next shot, etc.
Continuity mistake: When Tara, Sam and Ritchie enter the party at the end of the film, we see some people cheering for Tara's entrance. It then cuts to a wide shot, and all of the cheering extras/people are suddenly standing in slightly different places and in different configurations. (Likely they were told to wander around during the shots and just happened to end up in different places during different takes.)
Continuity mistake: When Chad is being chased by Ghostface, at one point he trips and falls next to some hay/leaves, then gets back up. As he is running, the amount of hay/leaves on him increases between cuts.
Continuity mistake: When Chad and Mindy get into a little argument about Chad going to look for Liv, when Minday says "Because she's probably already dead," she goes from looking forward to looking at Chad between cuts. Additionally, between cuts, she's also holding her beer bottle a bit differently, and the way the bag of chips next to her is open is slightly different.
Continuity mistake: When Sidney stands up at the hospital to meet Samantha, in the first shot her hand is up by her head, but in the next suddenly it's down on the armrest.
Continuity mistake: When Sidney meets Gale at the hospital and they hug, Gale's arms around Sidney change positions repeatedly in different shots, depending on the angle.
Answer: As far as I can tell, It's never stated in the movie how he found out about that. Maybe Sam told him off screen when he "learned " that Billy Loomis was Sam's biological father.