Except the client can act as a server once you start thinking about localStorage caching. Form/input validation is another thing which is really useful to have on both the client and server and benefits greatly from code sharing.
Validation is also two different concerns if you compare serverside vs clientside.
http://stackoverflow.com/questions/162159/javascript-client-...
Basically: Client side validation is about user experience, Server side is about security. I'm hard pressed to believe you can get both with the same code.
I also don't see how localStorage is relevant to code sharing between client and server.