If there are any mechanical problems in the pumps, gimbals, seals or other components there would be a record, perhaps the only one that would survive an explosion. Anything like vibrations or other mechanical stresses may also give clues as to the operation of the engine and perhaps suggest potential problems or fixes.

The other area of interest would be in the rocket plume or exhaust itself. This is a high-velocity fluid that is probably prone to turbulence, shock waves and high-energy acoustic phenomena or other instabilities that could either destroy the engine, or reduce its efficiency. I've noted that in the exhaust of aircraft jet engines, particularly when their afterburners are cranked up, you can sometimes see standing waves and other weird geometrical shapes and patterns (shock diamonds) in the flames.

https://en.wikipedia.org/wiki/Shock_diamond

How the exhaust is flowing can probably tell you a lot about conditions in the combustion chamber itself, especially under different operating conditions, and help the engineers optimize parameters for safer and more efficient burning.

Maybe TB could step in here for us. He probably knows quite a bit about this kind of engine development.