I'm going to assume you've read the
exporting a model as a map tutorial here? (and the
advanced section as well). If not you *
need* to read those to fully understand what's going on when you make a level in Blender. You also need to know the basics of building Q3 maps using Radiant.
The key to the process is to understand how the Quake 3 game engine works (via Radiant), not how Blender works. This means everything in Blender
must be in a format that's compatible with the brush volumes that Radiant uses, so, while you can technically use sub-surf to make your mesh, the result has to be reduced down to very simple blocks, shapes and forms, if you don't do that you'll end up with errors including what you've mentioned above - the result of 'broken' or 'corrupt' brush data.
Basically, buildings and flat (axial) surfaces can be exported as brush-based levels using the exporter. Complex, curved, or organic shapes can't so
must be exported as separate models (ASE) because brush volumes can't handle complex surfaces like those.
Post a screenshot of what you're trying to export if you still have problems.
PS Welcome to the forum. I deleted the duplicate post for you, only need the one