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.
Other mistake: In the hospital scene where Tom Smith, Mr. and Mrs. Howard and the groom are in the waiting room, it is mentioned that the evidence of the surgery taking time is noticeable by the light changing where Mr. Smith remains in the morning. In Seabiscuit, Mr. Howard, or Jeff Bridges, waits all night long to hear the results of the surgery, not Tom Smith.
Other mistake: Red Pollard's operation for his injured leg occurs over many hours (as evidenced by the changing light and darkness on Tom Smith as he waits for the results.) Yet when the doctor appears to tell Smith that Pollard will walk again, he seems to be freshly shaven. Surely if he had just been involved in a lengthy surgical procedure, he would not have had time to shave.
Answer: Red asked for $10 because he needed to see a dentist, and Howard gave him $20.