I don't know how, when, or why, but it on a recent WordPress upgrade for one of our sites, we had noted a good number of new 404s.
It appears that some of the "base URLs" had changed at some point along the line.
Luckily, we have the Apache RewriteRule on our side. Here's a few rules that helped reduce 404s and direct search engines and users appropriately:
RewriteRule ^/blog/categories/(.*) /blog/category/$1 [L,R=301]
RewriteRule ^/blog/(rss|RSS) /blog/feed/rss [L,R=301]
RewriteCond %{QUERY_STRING} getTags=(.*)
RewriteRule ^/blog/search /blog/tag/%1? [R=301,L]