Other mistake: Every time somebody climbs to the attic in the "lake house", you see a small, dark, enclosed chamber with some abandoned stuff. However, as soon as you see the "lake house" from the outside, it is a single-level construction entirely made of glass, with no inside staircase or ladder, and three smaller glasshouses on the roof. There is not a single wooden panel to enclose the attic, nor any construction in the house that looks like it could be that attic.
Suggested correction: It's not a "dark, enclosed chamber"; it's a glass surround with part of the windows darkened, but others letting light in. The ladder is shown near the end of the movie (when he's putting the box of letters away) to fold up into a small space, and the "attic" is merely a small space, easily the height of the roof plus one of the glass bits you can see from outside the house.
After looking at many photos of the house, there is no space for the attic.
Other mistake: In the hospital, when Alex's father takes the cup of coffee, it is obvious that there is nothing in the cup. He tilts it quite far back - if it had been full of coffee, most of it would have poured down his chest.
