In my wordpress blog I used Social Media Tabs (SMT) with Google +. When I inspected the network traffic with Mozilla's Firebug, my webserver produced a malformed GET request directed to googleapi.
The request was:
https://www.googleapis.com/plus/v1/people//activities/public?callback=jquery ... and so on. The GET request was malformed because it showed two consecutive slashes in the middle (...people//activities...). Consequently, the request failed and the response code was 404.
For me it appears to be a bug in SMT. Anyway, SMT seems to be the source of this request.