Any tag for language-specific puns/jokes?

There's definitely many pun posts that require some explanation (not every joke is so "fortunate" as post #655825), but even beyond wordplay, there's gotta be many posts that require explanation to "get" in English.

Off-hand, should this be pursued, I'd say language_barrier, but that might seem like in-post characters having trouble with each other's words. Maybe translation_commentary as a broader scope? Or is there something like this in place that my brief searches didn't pop up?

(My vote) I think the pun tag is good enough. If the pun requires explanation for native speakers of English (this may apply to most of them) then the comments section of the post should be used for this. I've also seen translator notes used for this.

If an explanation isn't given then it's because no one with the ability to comment or add notes has gotten the pun or has bothered to explain it.

I'm in favour of a "there is an untranslatable joke/pun on this image" tag.

From your two comments, let's throw in some kinda "joke_explanation_request" dealie. Obviously not what it'd be called, but something like commentary_request doesn't fit the notion.

No, no real need for that. The only people who would know that there is an untranslatable joke on the page is the translator, and we already have standards translation quality, which implies explaining when a simple translation just won't work.