OK running a valve amp into the wrong load (usually too high a load) can certainly damage your amp.
Using an appropriately rated resistive dummy load is the safest way to run your amplifier (although obviously it won't produce any noise).
Using a purely resistive load, the current and voltage outputs from the amp are in phase so all the amp output power is dissipated in the load rather than shared between the load and the valves as with a reactive load (ie a speaker).
Reactive loads can also cause amps to become unstable (oscillate).
Most attenuators on the market present a mainly resistive load to the amp. One exception is the Marshall power brake, which does not limit the high frequency rise in impedance.
The main "problems" with attenuators are:
1) They allow you to run the amp flat out. If the amp is well built with good quality transformers then this should be no problem, however many modern cheaper amps don't have good quality transformers (transformers are expensive so this is one area where manufacturers are looking to save money), and this may well cause the amp to be damaged. You will experience the same potential problem with running an amp flat out into a speaker cab, so this isn't really an "attenuator" problem.
2) The attenuator must be matched to the load. Generally unless the attenuator contains a matching transformer you can only use an attenuator at one load impedance ie if you have an 8 ohm attenuator you must use it with an 8 ohm amp output. This is really a user problem.
I usually recommend the THD Hotplate as I find this works well at modest attenuation, and presents an appropriate load to the amp. In my opinion attenuators generally don't sound great at high levels of attenuation.
