Other mistake: In the battle for Fredricksburg you can see streaks in the sky from jets.
Other mistake: When Leo X is hunting a wild pig, a poem is recited which mentions a boar (at least in the german version). But while the pig is running you can see it is a sow (from its longish nose). After the pig is hit, you can even see the teats. In the next shot the sow is supposed to look like a boar: It now has the characteristic big teeth of a boar.
Other mistake: When Marcela and Howard are viewing Seabiscuit for the first time (when he's weaving all over the place) it looks like it was done before as Seabiscuit follows a thin ribbon of disturbed ground that is weaving in and out. Its unlikely any other horse would be weaving like that.