How does radiolabeling work? Protein turnover can be measured by calculating the "decay" or loss of radio-labeled proteins in the blood, for example, but I am confused at how this calculation works. Wouldn't the radioactive isotope that you're using be decaying due to being unstable and not just due to protein turnover? Would you have to account for that in your calculations?

Technically yes, but practically it depends on what the half-life of your isotope is relative to the half-life of your protein. For example, tritium has a half-life of a little over 12 years, but most protein labeling experiments take place over only a few days at most (it depends on your protein). So while technically the tritium is decaying during your experiment, the amount of decay will be below your detection limit, and therefore is negligible over the course of the experiment.

So basically it works best to choose an isotope that will not appreciably decay over the time course of your experiment so you don't have to worry about it. If this is not possible, then yes, you would need to correct for this.