Factual error: In the scene in the park where Ben does his fake proposal bit and asks Lindsey if she'll go to opening day with him, the ticket is for Tuesday April 11th. It's obviously fake for two reasons. First, the Red Sox opening day in 2004 was April 9th, not the 11th. Second, April 11th, 2004, was a Sunday, not a Tuesday.
Continuity mistake: When Lindsey is at her parent's house during spring break, they are discussing her father's hair. In the shot when her mother opens the fridge there are only 5 cookies on the plate, but when the shot changes and Lindsey is grabbing some cookies there is a whole plate of them. And the honey pot is missing too.
Factual error: When Ben and Lindsey have their fight over going to Paris, Ben says he can't because the Mariners are coming to town (his schedule on the chalkboard says 9th-12th). The Sox did play the Mariners on the 9th-12th, but it was in Seattle, not Boston. Also, when Lindsey says "Pedro's pitching Friday", Ben answers, "Saturday, Schilling's on Friday". Schilling did pitch that Friday, but Bronson Arroyo was the Boston starter on Saturday. Pedro Martinez didn't pitch again until the 14th, against the Devil Rays.
Other mistake: Near the end when Lindsey goes to Fenway to stop Ben from selling his tickets, she borrows binoculars from someone to find him across the field. She's looking through the wrong end. The way she's holding them, everything would look tiny, and yet she still sees him.
Factual error: Ben talked about going down to Red Sox spring training during "Easter vacation." Boston schools do not get Easter vacation. They take a week off in February and a week off in April. February is too early for spring training (and Easter, for that matter), while April vacation is during the regular season.
Plot hole: After Lindsey is seen getting an MRI scan, Ben is in her kitchen and receives a phone call from Troy saying that Lindsey is on TV. But when Ben turns the TV on, the news anchor is just introducing the story about Lindsey. There's no way Troy could have already seen her on TV and had the time to make the phone call.