I am a bridge inspector in Minnesota, and while we don't look at railroad bridges (they are inspected by the owning railroads), I do know a little bit about steel structures. Obviously, I can't make an accurate assessment based on a few photos, but outside of needing a good paint job, I don't see anything alarming here.
Much of the rust is simple surface corrosion, which has a minimal effect on the strength of the bridge. More advanced corrosion, such as the flaking rust seen in the 3rd and 4th photos, appears to be confined mostly to the diagonal bracing across the bottom. This bracing serves to help stabilize the main girders and carry loads due to wind, but it is not a primary structural element.
The corrosion, while not serious, will continue to grow and eventually may impact the strength of the bridge. It really should be cleaned and painted before that happens.