You can even use 1 install of q3.
Always have a clean baseq3 and put maps and stuff in a folder in your Quake III Arena folder.
You can start q3 using a .bat with the quake3.exe +set game foldername syntax in it.
Even works with mods.
Use example: quake3.exe +set basegame modname +set game foldername
If you want to test your map, then simply run q3.

Btw. For GtkRadiant you'll need a second install of q3 to make maps in...
Edited 12.39 hours after the original posting.

You can use one computer to both developed and test. Here is how.

Create a new directory and call it something like "quake 3 clean". In that folder, create a "baseq3" directory.

In the baseq3 folder, place a copy of all the "pak*.pk3" files and nothing else. In the "quake 3 clean" directory, place a copy of the main "quake3.exe". Click the "quake3.exe" to start a clean copy of the game. When you are asked for a CD key, just press ESC.

To test your map, place your pk3 in the clean baseq3 and nothing else. Be sure to only keep what you are testing in this clean version.

@KommissarReb, It's most likely due to the fact of custom textures being added to the map from either other maps themselves, or from texture packs such as the MapMedia pack which are the cause of such issues.

Some people don't test out their new maps on a clean install but instead, test them out on a used install with other map .pk3 files such as those mentioned above residing within the base folder and as a result, they don't see the missing textures. However, you also have people who don't even test the maps in a run through which doesn't help the integrity of the publicly releases map.

Why would anyone submit their map with missing textures? Its one of the things that deter me the most from downloading. Don't these people test their stuff before submitting?