Really, to me anyway, the biggest hazard is dropping one or otherwise breaking it. The vacuum is extremely high so when they shatter the glass, even the thick face glass, has a tendency to fly around like bullets. When I was in electronics school the most common way to sabotage a CRT was simply apply 110 volts to the heater which blew it out and made the tube useless. Since we were all paying for the privilege of being in class in the first place, anybody that did that, sabotaged/destroyed a CRT, equipment or project, didn't last very long. There were too many of us that were serious about learning.
We had a teacher who was sort of an idiot, why he was ever hired is beyond me. Anyhow, he ended up in charge of equipment maintenance. We filmed him "drop testing" oscilloscopes, VTVMs, signal generators, counters and power supplies off the roof. He found they survived falls off a work bench so he moved "up" to the roof. The administrators couldn't understand how the test equipment was getting damaged that badly, until we, a couple of the students, showed them the film. It was very frustrating to me as a student since he was destroying the equipment we needed to learn with. The temptation to "administer the beating" was very great, but I did and do value my freedom.
I don't know who supervised the kids in the day class, but I will tell you that the night class (adults) didn't like how our equipment was continually sabotaged.
I've seen a lot of test equipment banged around when I was in the Navy. I was amazed what it would go through and still keep ticking!