Short answer: Yes. Long answer: Mental illnesses (Especially PTSD and depression) are common traits in a lot of Gintama's recurring characters, and they're all very diverse so while you have someone like Takasugi (A man whom trauma turned into an aggressive, violent and extremist person) you also have someone like Gintoki (Went through similar struggles as Takasugi but is a good and positive person who tries his best to live a good life). Worth mentioning that even Takasugi is not completely villanized by the plot as it tries to make you simpatize with him until the end.
a relatively minor character in the yoshiwara in flames arc (~ep. 139) is shown to be permanently disabled after her achilles tendons were severed in the past.
Nothing explicit or especially triggering, but a side character's main line is insisting he's not a lolicon, but a feminist (and then acting creepy towards young girls)
Gintoki is addicted to Pachinko games, which often makes him lose all his money. Lots of characters are also addicted to alcohol and tobacco but that's either played as comic relief or for aesthetic reasons, it's not serious and no one gets hurt by it
Sacchan, Gintoki's stalker, is into BDSM and projects all her fantasies onto him all the time. Also worth mentioning that the entire Yoshiwara city deals with women who were kidnapped and forced into prostituition.
It turns into one of the frequent running jokes basically throughout the show with multiple characters, can be heard and seen but it’s blurred/pixelated all the time. Personally as an emetophobe it doesnt turn me away from the show at all but the frequency of the exposure can be too much for some people. The only time its not visually censored is when shinpachi v* very briefly (spoilers:) while him and kagura are fighting abuto and abuto thrusts shinpachis body with the handle of his weapon into the ceiling. It was just some liquid though.