Character mistake: Sid deduces that Billy could be the killer because he could have used his phone call from jail to make the threatening call. However, the deduction has to be incorrect, since if it was really Billy, he could have never used the voice-changing device.
Suggested correction: This will sound pedantic (hey, it's MovieMistakes.com, we're entitled), but I don't think this is what is meant by a character mistake. Sidney isn't presenting an erroneous fact that goes uncorrected, she's explaining an idea that had crossed her mind. Billy immediately gives a plausible response and by the end of the film it's evident who'd called her. The takeaway isn't that Billy could still be the killer but that Sidney can't help but suspect him despite their reconciliation.
Character mistake: When they are surprised by Gale, Billy angrily says to Stu "Man, I thought she was dead." To which Stu replies "She looked dead, man. Still does." However, Stu didn't have time to check on Gale, since she crashed the vehicle moments before Sidney is attacked by a Ghostface that had to be Stu himself (since he does the quick clothes switch coming from the car).
Character mistake: Sidney asks on the porch why Cotton couldn't prove that he was having an affair with her mom. Tatum's answer is "Well, you can't prove a rumor. That's why it's a rumor." That's quite the preposterous answer, especially since the point she wants to make is that it was not in fact 'just' a rumor.
Suggested correction: Tatum isn't trying to argue with Sidney. Tatum agrees that she doesn't know the truth about her mother's infidelity and certainly can't prove anything. Rather, what Tatum is trying to tell her - gently and somewhat indirectly - is that she believes the rumors, which is distinct from knowing the facts.