I found part of the problem, and it was the zimbraProxyAllowedDomains setting in the COS. I compared the entries in the default COS to the entries in all my custom COSs, and discovered all my custom COSs were short about a dozen or so entries compared to the default COS.
I added all the missing entries and now the Yahoo! Local button works.
zmprov mc COS zimbraProxyAllowedDomains value1 zimbraProxyAllowedDomains value2 zimbraProxyAllowedDomains value3 etc.........
...on every mailbox server. Problem is all it brings up is a blank map page. Anyone know how to fix that?
zmprov fc cos COSNAME