I tried to use WinRoute to inspect the routing table on my Exchange Server 2003 system, but the tool just displays garbage or else crashes. However, email seems to be flowing normally. What's going on?

I'm guessing that you performed an in-place Exchange 2003 upgrade. In that situation, the Exchange 2000 Server version of WinRoute can't handle the updated routing table format that Exchange 2003 uses. You'll need to replace the version of WinRoute that's on your machine with the one that's on the Exchange 2003 CD-ROM.