Backup/Restore "Duplicates" and Broken "Content and Structure" (Settings.aspx)

This took a couple hours of staring at things and looking at every side of everything. I had used STSADM to back up a site and restore it to another site collection. This went pretty well, except for two problems:

1. Two of the lists showed up twice in the "All Site Content" (viewlsts.aspx) and
2. Content and Structure (settings.aspx) would error

#1 Symptoms
I tried deleting one of the lists. Oops. It deleted both (there really only was one). Hooray for the Recycle Bin!
The allitems.aspx for each list showed two web parts for the list (this is significant).

#2 Symptoms
You could navigate to any of the lists and stuff if you opened Content and Structure from another subsite, but you could not get to the root of this site.

Fix:
Delete the extra (duplicate) webparts from the allitems.aspx and all three problems went away.

Why? Ha! You tell me! But I am happier, and the users are happier. I'm just not very warm and fuzzy (welcome to my life with SharePoint).