One thing they didn't explain.

It's likely he completed rudimentary agent training, but his inability to properly use a gun meant he couldn't become a field agent. But because of his moderate competence in clerical duties he was given office assignments. Basically, as long as he wasn't actually in charge of anything, and was merely a cog, he did fine.

The real question isn't how he remained employed by MI7 for so long... but why they decided to have him handle the security at Agent One's funeral. I can only surmise that Agent One's legendary reputation led to the higher ups forbidding Johnny from being a pallbearer, reserving that honor only for the other, competent field agents; with the unfortunate outcome being that with all the actual competent guys handling the carrying of the casket, only Johnny and Bough were available to handle security.

"I mean, really, how many times will you look under Jabba's manboobs?"