Odds of Getting In
Since the first step is usually "get a job in a mine," that part should be no sweat. Well, no sweat during the interview anyway, but probably a lot of sweat once you start working. (No air conditioning in those mines, go figure.) After that, it's the simple matter of learning about mine safety and engineering that'll get you the inspector position.
With the proper skills, you can get a job working mine safety, but you may have to wait a bit for a federal gig to open up. The MHSA has a fairly direct application process, so if you stay up on the announcements, you'll know when they have a vacancy. Then you just need to apply, but first check to see if the vacancy had anything to do with a mine safety issue. Just a tip.