Factual error: Scott Hatteberg shouldn't have had to realize he could increase his chances of getting on base by taking more pitches and getting walks; in real life, he was always willing to take called strikes instead of swinging at pitches he knew he couldn't make contact with. That ability to take a lot of pitches and get on base was the primary reason Billy Beane was so eager to sign him in the first place.
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Factual error: Boston Redsox stadium did not look like that when Billy visited it in the movie. Fenway Park has gone through multiple renovations since then. The most obvious errors included the concessions section he enters Fenway through was newly renovated since '02, the first shot of Fenway includes the '04 & '07 banners, and a later shot included the wall with the monster seats, which did not yet exist.
Factual error: When Billy Beane is listening to Game 5 of the 2002 ALDS on his portable radio, we should either be hearing the Athletics radio announcers or ESPN Radio's coverage. Instead, we keep hearing the voice of Thom Brennaman, who was calling the game on television for the Fox network.