The scene where Richard breaks down after seeing the dress is supposed to have happened before he comes home and happens because he realizes that he has caught himself thinking about Arline in the present when she has passed on. This is mentioned in "Surely You're Joking Mr. Feynman", .
The abacus scene is also accurate but Richard is quoted as saying from "Surely You're Joking Mr. Feynman" that he knew logarithms so he could calculate the cube root of 1729.03 unlike the man with the beads.
The gate scene at Los Alamos is accurate and Richard had many more pranks that he pulled while working there. Most notably he picked locks. The one unique combination of locks was a series of file cabinets in a mathematicians office where the combinations began with the first few digits of the natural logarithm of e.
In the scene where Richard is pulling the wagon with his dad, according to "Surely You're Joking Mr. Feynman", he not only asks about the movement of the ball but also asks about why things fall. Less the gravity discussion this scene is actually what happened.
Arline's death occurs when Richard is still working at Los Alamos this is written in "Surely You're Joking Mr. Feynman". When Richard returns to work his colleagues think he is crazy because his wife has just died and he is working.