The dog was the silliest mistake... By far.
I know the movie is pretty 'fantastic' and I don't mind that everything in it is 'unreal', but they could have "trimmed the edges" with the whole dog situation. Here's my point:
In 2004, Alex rescues a stray dog. When he moves out of his lake house, circa '05/'06, he ends up leaving the dog behind for some reason. Kate, then, moves in and keeps the dog.
Now a little timeline:
1 - A dog shows up at the lake house during Winter 03/04 and Alex takes her in.
2 - Kate (in 2006) is browsing through old pictures and warns Alex there'll be a late snowfall in Spring/04, then shows the picture to that same dog (that is now hers) and asks: "You were not happy. Remember that?"
How could the dog be in the Spring/04 picture with her, if she was obviously still Alex's dog during that time?!?
3 - Kate (again, in 2006) tells Alex they must have the same dog. She says: "I don't know why, but I call her Jack."
4 - Alex (back in 2004) looks at the dog and calls out: "Jack?!", and the dog perks up, as if she recognized her name.
How can the dog 'know' a name that will only be given to her by Kate, in the future?
^ This and the nonexistent attic are two mistakes that could have easily been avoided by writers/director (or anyone who read the script and took a look at that house)...