The backstory of Dire Grove. The banshee came into existence because of a virgin sacrifice - one which involved the girl being sealed in an ice cave until she died. It Makes Sense in Context, but if you give it any thought after you solve the mystery... no wonder she wanted revenge!
Who exactly drew the sketches in Emma's diary in Ravenhearst? Especially the one of Charles about to kill her with a hatchet? It could be that the detective herself was the one who drew most of them, but there's no indication that she should have known that particular detail. Artistic license?
Fridge Brilliance: Escape reveals that ghosts can alter the appearance of objects, so maybe the "sketches" were blank paper until the Master Detective started reading the diary and Emma made the drawings appear.
What use is it to track down and dispose of the cursed horn from Shadow Lake, if the rest of the demon skeleton is left lying around where anyone who snoops around the ruined prison could find it?
In Escape, it's revealed that Victor went back in time at the end of Return and set up everything that happens in Escape. Why didn't he, say, prevent the Master Detective from solving the mystery in the original Ravenhearst? Or stop her from being born?
Dire Grove has one that makes no sense at all. In the early parts of the game, the videos the detective finds clearly show that next to no one has any interest in Allison's theory about Dire Grove, and evidence crops up that the people leading the archaeological dig on the site think she's more or less out of her mind. Cut to the end, and she's giving her presentation to a packed auditorium; she's rewarded with thunderous applause and cheering. Are we supposed to believe that these people believe she went through all of that?
In Madame Fate and the first Ravenhearst game we see that the Master Detective has an in with the Queen and she collects a lot of evidence in her logs. And as a detective in the service of the Queen, any notes she collects can be proven as evidence and can vouch for Allison and the other three students. Her endorsement and reputation can lend legitimacy to Allison's talk.