Dear, I am new to this forum and bought my first Omega watch on e-Bay a couple of days ago. I did some checks myself on this watch (dial, movement, back) using the book 'Omega - Reise durch die Zeit" (but the book does not seem to specifically cover exactly the model ST 135.003) and using the internet. Seamaster logo on the back seems a little bit different from the (small) logo in the book "Reise durch..." but is similar to logos I found on the internet attributed to similar ST 135.003 watches. I post some photos here and would be more than happy to hear your comments on this one.
Photo of the dial is poor quality, so it is impossible to say with 100 percent certainty that it is not a redial but it looks kosher. Movement, caseback and everything else checks out. I have the exact same model