Currently if I am in a particular department and viewing an Account or Contact, I can only see tickets that are from that department. This is all fine and good, but when I want to see tickets from another department, or ALL departments, when I switch the department, I am taken out of the Account/Contact.

This is very frustrating and makes for extra unnecessary clicks. I then have to search again for the Account/Contact within the new department. 

I think you should stay within the Account/Contact you are in when you switch departments. It should just reload the page with the appropriate tickets.