Mail goes from the same IP for all mail on that server. It won't be originating from one of your own (dedicated) IPs
The spam issue does affect us on shared servers. Luckily very infrequently (HN have got rather good at checking for out-of-date scripts and the likes). But, it does happen.
<touching wood>I can only remember once in the last very long time for my server... so I'm not complaining. Plus there was an MSN incident about 3 months ago, but that was MSN going bizerko.</touch wood>
(AOL and ComCast and sometime Yahoo don't count. They ban anything at the drop of a hat. I gave up on mail not going to those accounts ages ago.)