Save yourself some trouble. Let MC help you.
1) Remove the CD01 from the album title.
2) Place 1 in the Disc # field for each track on disc 1.
3) Rename using the following (example) directories Rule:
[album artist (auto)]\If(IsEmpty([Disc #],1), [Album], [Album] CD [Disc #])
This will place multiple artists albums in the directory called (Multiple Artists). You can of course modify the rule to place them another common directory, or you can use the "
Use 'Assorted' for [Artist] on multi-artist albums" instead of using Album Artist (auto) above.
It will also append the disc # to the title for you under the artists folders.
See images to see that the checkbox works, but you have to use [Artist].
You can rip the same way, so that discs are automatically located into the correct folder. To do this, don't rip immediately using the CD dialog that pops up, instead open the tag section of the action window and set the disc # field before the rip.
Setup your Options->File Location->Audio->Folder rule as above, then rips will go where you want.
When you ask about MC having a bad entry, are you referring to the track info that is found online when you enter a CD? If so, just update the track info to correct in your panes, and then right click the CD under Drives and Devices and Submit to Online Database.
btw. MC and MJ use YADB, not CDDB.
This might be useful:
http://wiki.jriver.com/index.php/Copy_%28Rip%29_CDs_to_Your_Computer