On a site mapped to a domain, when the header logo was clicked the viewer was sent to the Google Site URL instead of the domain URL. 

This has been fixed  You now are properly directed to the root level of the domain.

On mapped domains the header logo links to the sites.google.com URL instead of to the domain URL.  Until Google fixes this you can change the image to a header background image and it will no longer be a link.

First make sure that you have a copy of your logo image.
Click More (More actions)and select Edit Site Layout
Click anywhere on the header area
Select No logo
Click OK then Close
Then go to More click Manage site and select Colors and fonts
Scroll down to Site header background image and click it
Select Custom
Click Add file
Browse to your header image copy
Select Repeat: none, Horizontal Position: Left, center or right (as desired), Vertical Position: top, bottom or center (whichever works for you).
Click the Save Button at the top.

Then  remove the site name in the header. More>>Manage site, under Site name remove the check from "Show site name at top of pages".

See the issue reported at google-sites-issues. Star the issue to keep informed of any updates. Please do not post there that you are also affected...everyone is.