This is a sort of weird mystery I'm hoping someone can help solve for me.

All mail notifications from the Dude have the wrong time offset (+500 instead of -500). The local time is correct, the offset it just wrong.

Does the Dude have a setting for time somewhere?

I'm assuming I must have just set it up with the wrong time, but I can't find a time setting anywhere.

I do not have this problem. I am in US Central timezone. I am using Dude 4.0beta2 on Windows which has the correct timezone set in the OS. I use another host as a mail relay, but cannot check its timezone settings.

Here's an example email header I get from Dude:

Microsoft Mail Internet Headers Version 2.0
Received: from x by x with Microsoft SMTPSVC(6.0.3790.4675);
Fri, 14 Jan 2011 11:44:00 -0600
Received: from x by x with Microsoft SMTPSVC(6.0.3790.4675);
Fri, 14 Jan 2011 11:44:00 -0600
Date: Fri, 14 Jan 2011 23:43:59 +0600
X-OriginalArrivalTime: 14 Jan 2011 17:44:00.0069 (UTC) FILETIME=[A038F750:01CBB412]