How do I troubleshoot 3G connection on the iPhone? A particular client whom I provide email hosting support for, has problems connecting to the mail server using iPhone, via IMAP and on the China Mobile 3G data plan in China.

When asked over the phone what error message he got on the iPhone, he says iPhone only reports cannot connect to server. He says when using WiFi everything is fine.

In general, are there any ways I can troubleshoot the 3G network?
Wow, tough one. Tough because there are many unknowns in this equation... 

No way to know for sure if China Mobile is not causing the problem by blocking, for example, the ports required to connect to the mail server. The only way to test this would be to change the port settings on both the server and the client, I think. In theory, it is entirely possible for them to block ports they believe can be problematic or some other reason, although I don't see how blocking standard mail ports would be problematic and help their customers...

Are other services functioning properly when on 3G? Like web-surfing, app updates, chatting, etc.?

It might be a case where your client needs to contact China Mobile and ask them for a little help troubleshooting this problem on their side, just to be sure it's not their network that's causing the problem...