Is it right for Soldiers to post Military paperwork and photos of equipment on Social Media?

As with most things it depends. Anything containing FOUO, classified info or PII would violate a ton of regs. If the equipment isn't classified then no problems there. If the paperwork is scrubbed to remove PII and does not contain classification that is fine too. As long as they aren't crossing any lines like I mentioned, there is no issue. If someone doesn't like it, then they shouldn't look at it.

In matters of OPSEC or personal identifying information, it's an issue. If it's a matter of humor in uniform, then it's in the eye of the beholder.