If I upgrade from git 1.7 to git 1.8 on my server, do I have to update my repository too? Will a git 1.7 client work with a git 1.8 server and vice versa? Is there anything to be concerned about?
do I have to update my repository too?
No, the internal format of a repo remains compatible.
Will a git 1.7 client work with a git 1.8 server and vice versa?
Yes, there is little change in the transport protocol (mainly in http protocol).
The protocol capabilities don't mention any backward compatibility issue.