I am having the same problem as
http://support.addthis.com/customer/portal/questions/321190-addthis-linkedin-ssl-issue
When on the page with the AddThis page it give me an insecure content warning for:
The page at https://********.com/******* displayed insecure content from http://static01.linkedin.com/scds/common/u/img/sprite/sprite_connect_v12.png.
I think its similar to the issue raised in this thread:
http://developer.linkedin.com/thread/3047