Continuity mistake: When Bullock is warning Reeves of the coming winter blizzard, she is looking through pictures that depicted her and her friends enjoying the snow. She then turns to the dog and asks "Remember that day? You were not happy". However it's revealed that both characters have the same dog, given to Bullock's boyfriend by Reeves, so when the snow happened in Reeves' time - 2004 - the dog was with him.
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.
Plot hole: Kate is in the future and has named the dog Jack and informs Alex of this in a letter, which he receives in a magic time-travel mailbox. Alex adopts this same dog in the past, before the dog has ever met Kate. Jack tests out the name "Jack" on the dog, and the dog reacts to this name. The dog should not know this name as it hasn't yet met Kate. This is backwards. Alex should have been the one to tell Kate of a name he gave to the dog, and she should have been the one to test it on the dog.
Plot hole: When Kate went to the aid of the man lying in the street, she was very upset about his death. Would she not have got his name being that she works in a hospital? Also she could have easily Googled him in 2006 to find out where he was or that he had died already. It seemed an obvious ending that she would save his life to change history.
Continuity mistake: During the scene when Alex and Mona are riding in the truck with Jack the dog in the back end, the dog vanishes during several shots in which she should be visible.
Revealing mistake: Kate's birthday is July 10th. When she is (with long hair) outside on the patio with Alex, you can see their breath as they talk, and there is not a living thing in the back yard, it's all dormant (as in late fall/winter).
Continuity mistake: In the lunch scene where Sandra is showing her mom the letter she says the year is 2006. The poster behind her is advertising tickets for the year 2004.
Revealing mistake: When Kate kisses Morgan in front of 1620 N. Racine, the camera moves up through the branches of a tree. You can see one of the lower branches shake when it is bumped by the crane. (01:17:20)