Wrong Favicons in Firefox

Close firefox, delete %AppData%\Mozilla\Firefox\Profiles\<your profile>\favicons.sqlite

This is easier to do than peqhusus's solution, but it does mean you'll lose all cached favicons and have to reload your bookmarks to get the icons again.

This may not be the best solution if you are only slightly annoyed...

What I usually do when this happens is go to

Bookmarks --> Show All Bookmarks --> Import and Backup --> Export Bookmarks to HTML file

Then open the bookmarks file, find the corresponding bookmark entry, then change ICON_URI="{URL}" ICON="data:image/png;base64,{data}

to the URL of the icon and the base 64 encoded icon in png format

Then import the modified bookmarks file back into Firefox