I'm glad this is being discussed again; I have the same issues. I'm new to the game, so I've been trying to accomplish these things pretty vigorously.
I had the issue last week, where I was to test the Hammer while in orbit at a certain alt. Once I got green checkmarks across the board, nothing I tried (and I tried a half-a-thousand times) managed to succeed. I finally gave up.
I just started a new career and the second mission I accepted was exactly what was mentioned in this thread, and so very simple.
"Test the FLEA at the launch site". That's it. Simple. Going to the launch site, immediately the required conditions are green, but the test will not succeed. I click on the booster and choose "run test" or "activate engine". Nothing. I try staging (which is the first stage anyway). Nothing. I try with 10% thrust; it just sits there, all green, without success. I even tried a second flea in series, so I could stage once first... Nothing. All green... Fail.
I don't want to be 'that guy', but this is either a bug, or there's some secret condition that isn't displayed, like your kerbal must be an engineer (except, I tested that too), or your Kerbal must be a level 2 (didn't test that yet)...
Anyway, I really like this game, but there's some issues here. Add the steep learning curve and I suspect a lot of people are just going to give up!
Anyone have any input?
Thanks,
DbulHelix