Kill the Spare
We do know from Beedle the Bard that Care of Magical Creatures was taught before Marauder Era as was Herbology because Dumbledore's notes mention Kettleburn and Beery (Herbology teacher) and this is when Dumbledore is still the Transfiguration Professor. There was a DADA teacher in Voldemort's time too. I would imagine that the classes have stayed pretty much the same, although I wondered whether in the past Occlumency was taught.
Lupin certainly knows that Snape is a superb 'Occlumens' so maybe it was an option during their time at Hogwarts.
Banner by the opaleye
Hmm, I've been wondering the same thing. I think the wizarding world is not very...um, change-able. It seems a bit rigid, so it's likely that the same classes we saw during the books were taught during the Marauders' time. Maybe some subjects, like in potions, had less information than in Harry's time: maybe the wolfbane potion wasn't invented yet, or maybe potion masters hadn't discovered certain antidotes and etc.
I also thought that maybe some subjects taught in Hogwarts changed a little with every headmaster. Of course, for the Marauders, subjects would have had the same sort of focus than during Harry's years at school, seeing that Dumbledore was headmaster back then too. But maybe during, say, Phinneas Black's time there was a darker focus..or more focus on dark arts or things like that. I can definitely imagine Occlumency and Legilimence being taught during his time as headmaster.
First Brush With A Dementor
I think we can be quite sure that Professor Sprout has been Herbology teacher for the Marauders. Dumbledore mentions a Herbology Professor called Beery, who taught when Dumbledore himself was Transfiguration Teacher, so that is some time up to 1956. Professor Sprout definitely teaches in 1991, and it certainly isn't her first year, plus she's not the youngest anymore, as Neville is teaching in 2017 and seems to have done so for at least a year (because Harry's son refers to him being a Professor in the classroom, so he must have experienced that situation).
Either there was a teacher in between who only taught for a rather short period, or Sprout has been teaching since the 50's. This means she'd be roughly in her 40s when she teaches the Marauders, and in her 60s (I'm not that good ad math) when she teaches Harry - assuming that teaching was her first career. Add ten years for travelling, maybe some healer-equivalent jobs, research... So seeing how Dumbledore is 150, it's not that unlikely. Also then Sprout would have been teaching for about the same time as McGonnagall.
But she was definitely younger in the Marauders Era, so there might be physical differences - maybe she was thinner, her hair still had some colour...