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.
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.Uncel Mark
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.
Kate: Life is not a book, Alex. And it can be over in a second. I was having lunch with my mother at Daley Plaza and a man was killed right in front of me. He died in my arms. And I thought, "It can't end just like that on Valentine's Day." And I thought about all the people who love him, waiting at home, who will never see him again. And then I thought, "What if there is no one? What if you live your whole life and no one is waiting?"
Question: Why did Alex have to wait until Valentine's Day 2008 to meet Kate? Even assuming for the sake of argument that the "time-traveling" letters stopped after Alex avoided the bus accident on "his" Valentine's Day 2006, Alex certainly knew how to find Kate at that time - and vice versa. The two-year gap where Kate had not known about Alex had closed by that time, and each knew about the other.
Question: What happened to Jack the dog? Last she was seen was when Jack showed up at Kate's boyfriend's work. The boyfriend said "I know you." and looked back at Alex walking away. I assume that's how Kate got the dog. But Jack isn't really seen in Kate's time much, after the chess game.