Other mistake: When Ellen gets back to the inn after fetching the homeless guy, her coat has barely any snow on it when she enters. With the kind of snowstorm shown, she should have a ton of it. Same if not worse for Jake who came in before her. He has some snow on his arms, but none on his back - and he spent his time outside packing firewood with no time to wipe clean. (00:46:20)
Other mistake: Jake walks up to "Ellie"'s room to take her to the cafe that is just around the corner. It is plain day, but when they get to the place, it's dark. She does comment that it gets dark fast - but we talk about a day-to-night difference; his aunt even offers him dinner. (00:22:30)