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: At the Gazette office, as Ms. Rees-Jones watches, Steven scrolls up the next front page of the Gazette on his PC and under the photo of Chuck Hughes it reads, "...dead at age 37." However, when Frank gets into his car after being kicked out of the cemetery, under the current Gazette headline it reads, "30 yr. old Chuck Hughes who died of a mysterious heart ailment..." (00:03:10 - 00:05:30)