I recently bought a used bach tr300 trumpet off ebay and it seems to have sound problems when I try blowing notes with the first and third valves depressed. All other notes seem to sound really good. The trumpet looks like it is in fairly good condition a few minor scratches, and valves move freely. I was wondering if this is a common problem and if there is anyway to repair.

Without us being able to actually look at the horn ourselves, or test it out, there isn't much we can do to help you.
Take it to either
1) an experienced trumpet player. Make sure it's someone who is familiar with the inner workings of trumpets. If they say there's a problem, or can't really help you, take it to
2) your local music store. They'll be able to look at the inside of the horn, test it, and see if there's a problem, and if there IS a problem, they can fix it.