Should I pause mirroring when I reboot the witness server? So I know that when patching the two main database servers (SQL Server for the record) you do the mirror, failover and then when it's all caught up do the new mirror, but what about the witness box? Is it safe just to patch and then restart it and (in theory) it will just pick up again?
You must do this in order if you want to update the Principal, Mirror and Witness:


Switch from high-performance mode to high safety mode (if you are using this mode)
Remove the Witness
Upgrade the Witness (anytime between 2 and 9, see below)
Upgrade the Mirror(s)
Wait until Mirror(s) is(are) synchronized and manually fail Primary over 
Upgrade the Primary
Upgrade the Witness (if not already done between 2 and 9)
Switch back to high-performance mode (if required)
Add the Witness