Maintenance/Repair (Proper way to take care of boxing gloves and wrist wraps after use?)
Definitely. While it could be argued that any DIY board or the like could conceivably offer these suggestions, they would not necessarily have the requisite background to know how the application of martial arts affects them. For example, a question was asked about bokken and jo restoration, which, to a DIYer might appear to be about how to restore a wood object. To us, however, there are issues of impact, slippage, splintering, etc. that must be taken into account. Your average punter is not going to have any clue as to how to properly sand down a bokken if he has no experience in how to use a bokken to combine with his experience of maintaining wood. The proper maintenance of a katana for use in kenjutsu is absolutely relevant.
Usage (How do I keep the bo staff from moving off centre as I train in twirling it?)
Definitely, of course... I think we need to push askers to be specific about what art, and clarifying what they mean by some of their terms; "twirling" (in this case) to me has a connotation of furigata, and the use of the wonderfully redundant "bo staff" suggested a Japanese martial art. It turned out the asker was referring to a style of Taijiquan he was learning (which would have carried more weight with the use of the proper term gun).
Construction (What's the best way to sew badges onto a uniform so they don't come off?)
This... might get a bit hairy... Sewing badges to withstand tearing off while training? That's an issue that you're drawing on the experience of martial artists – most patch sewers have no experience with the potential of them being torn off by another person. Further, many dojo have requirements about the neatness of stitching (maintaining a proper uniform) which would result in better ways to do what's being asked. However (and I say this training in ninpo taijutsu and ninjutsu), questions of the construction of shinobi shozoku and the various components should not apply, nor should the construction of SCA armor.
Recommendations (What is a good mat system for home MMA training?)
I'm a little spotty on this. Recommendation solicits opinion. If you're asking about the durability of a particular mat set, then this might be good. If you're asking about what to look for in choosing an iaito then it's on topic. If you use the term "best", it's probably subjective, and needs to be rephrased. We should be pushing for facts.
Legal/Philosophical/Rules (Are martial arts practice weapons regulated? [closed], also any questions about the legal requirements within a given art)
This is three things...
Legal – We should avoid anything resembling legal advise, or preface or caveat all of our answers with "Nothing in this answer is intended to be construed as legal advice. You should consult your own attorney." or similar.
Philosophical – I'm inclined to say yes, so long as it's not blatantly unrelated ("Does a dog have a Buddha nature?" is, aside from not being answerable, is completely off topic). In ninjutsu, there are concepts such as kuji-in, tenmon (astrology), and strong ties to mikkyo and the yamabushi. These are important because they were a manner in which the ninja decided how to approach a mission. Questions of mushin and zanshin are largely philosophical questions, and so long as the questions are intended to be answered without debate, they're fine.
*Rules – Specific tournaments (the Walla Walla Invitational of Aikijujutsu, if some such thing existed) would be far too localized [there's not a significant legitimate aikijujutsu presence in the US, an invitational would be exclusionary, etc.]. Olympic Taekwondo rules clarifications are common (and in fact those rules are adopted amongst many tournaments) and would make a fine question. If the history of a rule could be found (and thus the question could be answered), so long as the rule is not too localized, the question would be fine.
History (Why are firearms not part of the martial arts world?)
If you want to understand the future, look to the past. Martial arts are a historical study; we're learning something created by someone in the past, even if it is the recent past. The reasons for its development and the way its evolved over time are vital to a proper understanding of the art. I see few reasons this should ever be declared off-topic unless too broad a question, too localized ("Joe Blow, who lives next door to me, created Hoo-fong-pu Kung-fu, what historical basis is there for this art?"), or unanswerable.