Yes they do (resource problems). If you hold your "Home" button you'll see the last running 6 apps. Since, with android, most apps you can't close: those are typically the actual running 6 apps on the system right now.

Now again, people have worked around this. Bloo, Meebo, eBuddy, etc register a service that constantly checks Facebook, IM's, etc for the information they need in order to notify you of their changes. And then, non network/constantly updated apps become a non-issue, because even if they aren't actively running they are in a saved state that the next time you look at it it's exactly like when you left it.

It would be really hard for me to come up with 7 active things for you to do in succession that could prove how it acts.

But, just as an example, I used to use AndChat all the time for IRC. I would try and leave AndChat connected all day long, but every time i went back to looking at it after a few hours I was disconnected. I had to manually reconnect because AndChat didn't reconnect for me. Contrast that to Xchat on my N900, I run it all day and yes, I lose connection, but it always reconnects for me. So when I look at my Xchat I'm always in the room (even if I haven't actually been there all day).

So .. multi-tasking on the N900 (at least for me) has definitely been far more consistent on the N900 than ever on my G1 (but, the G1 hardware also sucks.)