The SD card that came with my H2 is a pile of junk and slow. Get a
fast 2GB SD (or 4GB SDHC, Class 6) card and the "Invalid File" errors should diminish with non-native mp3 files. Notice I said "diminish". Generally, stay at 44.1 and the middle of the range of bitrates in stereo (as hartsook wrote) and you should have far fewer errors with non-native mp3 files.
The H2 really doesn't make a good iPod surrogate, as the almost illegible display is only for people with X Ray vision. It obviously can't make playlists and it can't recognize albums, unless they exist as one large mp3 file. Speaking of iPods, I'm surprised no one has suggested using an iPod in conjunction with the HV20. Logitec (not Logitech, unfortunately) makes a stereo microphone for iPods:
http://nexus404.com/Blog/2008/03/06/...-to-your-ipod/
as does Belkin and Griffin. Although I haven't tried any of them, in theory, you could use your iPod in the same manner as the Zoom H2. If anyone has tried this option, I would interested in what the sound quality is like.