I bet to Japanese people it'll age weirdly with the references it kept making to politicians and actors of the time.
I really enjoyed it when it wasn't trying to be a shonen jump anime. My favourite episodes like the Nabe Shogun bottle episode, or the several lazy animator episodes either with the drawing quality rock bottom or the paralysis with no animation at all.
I used to watch it on a service called something like animeftw or something that's no longer around on an xbox xbmc setup. So much nostalgia when I see screen caps.
There's some really obscure references in gintama, now maybe everyone in Japan is as well versed in old Japanese TV and cinema as Sorachi Hideaki? I think part of its appeal is it's esoteric references though.
As far as the puns go, I'll admit most fluent Japanese speakers understand them (I'm not fluent).