What are things to look for that would indicate that a valve train has instability issues (before an engine/component failure)? Parts inspection? A unique symptom from the way the engine is running?

I would say to put a dial indicator on the end of the rocker stud and see how much movement you have when you crank it over.

That wouldn't show an issue at higher rpm/load where it becomes a problem. I think you just need to go with proven combinations or a proven engine builder.

I agree with a proven combination. But that is the only way I know of to check for any valve train movement.

I understand the use proven parts and proven engine builder to minimize possibility of valve train instability in an engine.

The question is after the engine is built and running. Is there any indication of a harmonics related valve train instability that have also shown up on new parts such as the cam lobe, hydraulic lifter roller, push rod, valve spring, valve spring retainer and locks, valve, valve guide or roller rocker after lets say about 25 hours running or a dyno session or how the engine performs or running characteristics such as valve train noise if the engine has valve train instability?

Try taking off the spring retainers. See if you have to beat the locks out of them.

There was a video link posted recently in regards to that. It's amazing how much movement there can potentially be with simply rolling the engine over. Imagine what it's doing at 6,000 rpm. Can be time consuming and often overlooked but so important. Correct length pushrods for starters and offset rockers might be needed as well as stud girdles. If money isn't a factor I personally really like the Jesel sportsman series shaft rockers.

That's why I made sure I did girdles this time... I want it to be solid as a rock..

could you somehow hook an oscilloscope to the block to see if you have an odd major harmonic or something??

Run it till it breaks! Valvetrain stability is a relative thing , Even horrible setups are stable somewhere in there operating range.