Ooh, this is a fun one.
1. They can detect *very* minute amounts of material.
2. You can label specific atoms (say carbon-1 in glucose) to follow where each one goes.
3. A radioactive molecule is chemically exactly like the unlabeled form (this isn't really 100% true but for what you want it's close enough). Thus, it will behave just like the unlabeled form so you don't have to worry about effects due to the labeling itself.
4. Since carbon, hydrogen and phosphorus can be easily purchased in radioactive forms, you can make just about any biomolecule in a radioactive form.
1. Radioisotopes are rather expensive.
2. Radioisotopes are hazardous and must be handled with extreme care. By the same token, they present a disposal hazard.
3. Some radioisotopes (like P-32 and I-125) have short half-lives, so you have to use them quickly.
I'm a biochemist.