How to tell vacuum tube is gone bad??

Different tubes burn at different brightness levels. If you have 6 identical output tubes and there is a big difference in brightness then most likly the bias needs set.
The soot on the wall is common in tubes. Don't worry about it. This is unwanted gas in the tubes being burnt up when first firing up a tube.

The brightness of the various tubes are mostly a non-issue as this isn't an indication of the condition of the tube, but more related to where the plates and cathode are in relation to each other.

The soot on the glass is also of no concern. Mullards typically leave a very dark, smokey haze on the glass and that's normal. Small signal Mullards will often "flash" upon power up and that's just a design thing and not an indication of an arching tube.

Listening is the final and most important test.

Failing or aged tubes in general lose bass energy, the sound will tend to be harsh. If so, it is time to change them.

tube testing is often available at music stores for your guitar amp. if you've got used unit or used set of tubes, you can go and check there. in my area there are plenty of local small guitar shops and almost each have tube tester if you're not ready to get your personal. tube that went bad have a possibility to 'take away' other circuit elements such as capacitors or resistors in its power supply.

In my case a loud pop and a spark were a clue that I had tube failure