Elite Force can run into problems if too many pk3 files are installed at once. This has to do with the game opening file handles for each pk3 file present and hitting operating system limits. On Windows the limit is usually about 500 pk3 files, but it can vary on other operating systems.
There are two kinds of errors caused by being over the pak limit. The first is if you have too many paks in the baseEF folder alone, in which case the game won't run at all. The second case is if the combined number of paks in baseEF and a certain mod folder is over the limit, in which case you get an error when you connect to a server running that mod. This is why people sometimes have problems playing quake 3 maps that use the "q3maps" folder while other maps work fine.
Solution
The cMod client available here does not have a pak limit. However, if you prefer to use your current client, here are the instructions to clear out some paks to stay under the limit.
Step 1
The first step is to find where the game is storing pk3 files. There are three locations that typically might be used on Windows depending on your EF version and configuration.
Location 1 - Main game installation folder. If you did a default installation it might be located somewhere like "C:\Program Files (x86)\Raven\...". Or try right-clicking an EF icon and selecting "Open file location".
Location 2 - Virtual Store folder. In some cases the original EF client can store files in this location. Open a run box (Windows key + R) and type "%localappdata%\virtualstore", without the quotes. Check if any EF-related folders exist here.
Location 3 - Application Data folder. Some versions of ioEF save files here. To try opening this location, open a run box (Windows key + R) and type "%appdata%\stvef", without the quotes.
Step 2
Inside each location you should find subdirectories such as BaseEF and other directories that are used for mods. In general you can remove all pk3s from BaseEF except pak0.pk3, pak1.pk3, pak2.pk3, and pak3.pk3. You can remove mod folders such as q3maps entirely. Assuming the files originally came from server auto downloads they should simply be downloaded again if they are needed.
Be careful not to accidentally remove non-pk3 files, such as hmconfig.cfg, as that could cause all your settings to be reset.