I'd like to swap the crankset out - it's a Shimano Sora 30/42/52T
(FC3303). For example, I have seen a Shimano Ultegra with the same
30/42/52T (FC6503) on Craigslist. Are there any specific details I
need to be aware of matching up?
The main detail you will have to watch out for (as indicated by Kibbee) is whether the two cranks use the same bottom bracket. Crankset attachments are standardized; however, to paraphrase Tanenbaum, there are many standards to choose from :-).
To check whether a specific crank and bottom bracket match, you'll need to know some details about the bottom bracket, such as shaft length, attachment type (square, most common, or spline) and chainline. There are compatibility charts online to help you; a good one is Sheldon Brown's Bottom Bracket Size Database, which also lists the Shimano Sora and Ultegra.
Also, check whether the new crank is compatible with the chainrings. There are different attachment mechanisms in that area, too, so you may need to swap the chainrings along with the cranks.
If you want to play it safe, it's best to buy the part at a local shop. They can tell you whether it matches or not, and, most importantly, if they tell you it definitely matches and are wrong, they'll have to take it back. Also, they'll be able to answer your questions about mounting it - or mount it for you for a fee.
Finally, note that for some attachment mechanisms, you will need a special tool for removing the cranks, called an "crank puller". I think you don't need one for the Shimano Sora, as it is "self-pulling", but better check to be sure.
If I keep the same tooth count, will I have to worry about replacing the derailleurs?
No, the rest of the drive-train should not be affected, at least not of the new BB is fully compatible. If it has a different shaft length or chainline, there might be problems (so it's best to avoid that).