Not sure if it's still an issue, but some tips I've come across on the forums for speeding up the impossibly slow training of the military:
1) Make squads of 2~3 members each, to increase the odds of them sparring (which gives better training) and decrease the odds of them starting a demonstration, then waiting around doing nothing while one squad member finishes eating/drinking/sleeping to join them.
2) Make squads consist of people with as closely matched skills as possible, to decrease the odds of one trying to teach another some skill he is better in. E.G. if one is a Proficient Biter, and the other is a Dabbling Biter, they will waste a lot of time as the Proficient Biter slowly teaches the Dabbling Biter how to bite things.
3) Make squads all use the same weapon (related to rule 2)
4) If you trap a lot of wildlife/gobbos in cages, make a
Mass Pitting Room with an arena below that can be sealed off, and station a squad below, them dump in live training dummies (after you've stripped their weapons. For more training time, equip your squad with Training Weapons so bludgeoning the gobbos takes longer and gives more experience. To train marksdwarves, just dig out a small 1 tile wide corridor next to the arena and carve fortifications in the wall, so they shoot into the arena without getting hurt.)
5) Make sure everyone has weapons (if metal is scarce,
at least training weapons for training purposes), ammo (can be wood or bone for training), and is assigned to 'T'rain at a barracks, (can be one barracks for everyone, but you need several Archery Targets per Archery squad)
Once they're well trained, you can reorganise the squads however seems best for your strategies. Rules 1-3 have a surprisingly large impact. If you do happen to have some dwarves with extremely high combat skills, and some new recruits with very low skills, it's only worth putting them together in a 'teaching squad' if the veteran has a high 'Teacher' skill and the rookie has a high 'Student' skill (i.e., never). Usually you'll get faster gains by sticking two equals together and letting them spar. Sparring also won't happen much until they have at least some skill in a weapon, so maybe use rule 4) on recruits until they're at Novice level, then to sparring.
Before implementing some of these ideas my militia would take a decade or so to advance to 'Skilled Rank.' Now it's much faster, though nowhere near as fast as a danger room exploit. It's closer to the rate that most other skills progress at, if a little slower, so it feels 'as intended.'
If you're incredibly nerdy you can check out some specifics in
this thread investigating the different methods of training militia