Looks like EA is working overtime to fix all the problems people are experiencing with the game. They've just released patch 1.03 and they say patch 1.04 will follow real soon to fix even more problems.
The C&C3: Tiberium Wars Patch 1.03 fixes some multiplayer problems:
The easiest way to get the patch is through the automatic update engine or you can download it at this mirror.
Fixed an error that caused players to experience unexpected disconnections and freezes while in online lobbies and Automatch search. Fixed an error that prevented players in online lobbies from chatting globally after sending private messages to other players