Dont have a lot of experience but the obvious one would probably be when you lift it with the crane make sure you lift it correctly. Probably best to lift it at where the support locations facing the right way.
I have recently worked on the construction of a few box beam bridges. Here’s my experience with your issue:
Make sure your substructures are in the correction location!!! I had a project where the abutments were too far apart (by just less than a foot). Luckily, this was caught in the field before the beams were even fabricated. I was the design engineer for the project and also provided construction assistance. I was able to work with the fabricator to get the beams cast to the correct length to fit the constructed abutments. I would also say, make sure the abutment seat is wide enough for all the beams.
These checks, along with checking the seat elevations, should all be done before the substructures are even poured. But, but double checking them before the beams are set is a good idea. You should be able to find tolerances for the beam seats and such in your state DOT construction specifications.
You might what to post this question in the Bridge Engineering Forum. You might get a few more responses there.