We have a service desk that prioritises all the calls. They have a set of rules and guidelines but can also be guided by the caller as to what the priority should be. They log the call and then send it to the appropriate group. In my group, we have a different team member each weeks that checks all the calls that are logged to us. They will either assign it to a team member or re-direct it to another group if assigned incorrectly.
We use 4, 3, 2 & 1 as our priorities. For P1 and P2 calls, all managers get alerted. We have to respond quicker to P1 & P2 calls as these are watched closely.
My favourite error message is "the internet is down!"