Make sure the bike doesn't have vertical dropouts.
Make sure all your parts are the correct size for the frame and fit well with other compnents.
Make sure the frame doesn't have hole through it, or is bent.

Other than that... not much. I mean... if it works well, it will ride well. You can do it for really ****ing cheap also if you don't care about looks, performance and such, but since you want to race, you will want to get decent parts. I would suggest getting a low-end entry track frame if you are serious about starting to race, but if you don't have the money ($350 or so) you can just keep on with the conversion. Ask the mechanic you plan to go to all the questions you want. He will most likely answer them.