Glad you got it working! Always nice to recover and be able to continue with your work invested in upgrading vSphere. SSO centralizes authentication across all components (vCenter, Web Client, Inventory Service, Auto Deploy, etc.) So if SSO is not working/down or is not configured as you'd expect, it will prevent you from accessing a lot of resources in your VI.
I would definitely recommend reading through the materials on SSO, there's a lot of good info you can find in reference to the vSphere doc link from my earlier post, even if the material is a little dry :-)
The issue accessing the web client from remote devices is interesting. Hopefully it's working now? If not, might be worth investigating further. The web client is written I believe in Adobe Flash/Flex, and it's going to be the future of access to vCenter and ESXi hosts. The fat client is EOL after vSphere 5.1 according to VMware's release notes.
Take care!