Connection Issues:
1. Restart GMOD.
Fixed? If not:
2. Start your own multiplayer server and join the server you want from there.
Fixed? If not:
3. Close steam and go to your Steam directory ( Not Steamapps. ) and delete "ClientRegistry.blob" and let Steam update. Then do step two and most issues should be fixed.
Graphical Errors:
1. Restart the game and perhaps even you PC in the event that your graphics card is overheating.
Fixed? If not:
2. Go into your steam library, right click GMOD and select properties, navigate to game files and press: "Verify integrity of game cache."
Fixed? If not:
3. Delete Garrysmod in your games library and the folder in Steamapps and do a clean reinstall. ( This will make you loose all your files so back shit up! )