By far the most common fault with vacuum tube rectifiers is that the cathode will lose emission,so that the internal voltage drop of the device will increase to the point where they become unusable.
Occasionally,you will get a filament go open circuit,but that is a lot rarer,arc overs internally are extremely rare.
Vacuum tube (valve) rectifiers come in both directly heated & indirectly heated forms.
Mercury vapour rectifiers will arc between anode & cathode under certain circumstances,& usually have special protection circuits to prevent this becoming a sustained arc.
One nasty trick mercury vapour rectifiers had was of oscillating,if they haven't been warmed up properly.
Tube rectifiers in Broadcast & commercial equipment are obsolete,replaced by silicon rectifier stacks.Usually,even very old Transmitters were retrofitted with solid state devices.
The latest generation of TV & Broadcast Transmitters are mostly all solid state,whereas the previous generation was solid state up to the penultimate stage,then tube finals.
The tube final in a VHF TV transmitter is a pretty hard act to follow,with around 13dB of power gain in a 5MHz wide amplifier,20.000 hours average life,easy cooling with a large capacity blower.
A lot of the new solid state finals have gone "back to the future"with water cooling like that used in 1930s tube equipment,& very high power stuff in more recent years.