Hi,
Having explored Mount Wellington Mine via the main engine shaft (200 feet), before it was reopened, to adit level, I can state that there was no bad air at the time, even though the adit sumped a long way downstream, and no other shafts were open to improve aeration.
After the mine reopened, the very long upstream adit had dried out, and so with wet-suits on, the going was very hot indeed, which may have been partially due to bad air.
I never experienced noticable bad air anywhere underground, except for in an overpopulated air-bell in Swildon's Hole!
There was also a case of foul gas in Baker's Pit Cave, Devon, which lies beneath a fermenting refuse tip...until a second quarry entrance was blasted into, causing such strong air currents that the system dried out in about one year...
Radioactivity in granite mines has also been recorded, but not extensively monitored, except where uranium was worked.
But smoking in small chambers will rapidly foul up air, causing thick smog...
Generally speaking, columns of warm saturated air rise up out of shafts on cold days, sometimes for many hundreds of feet. This was how cavers noticed the world-record 'Pierre St Martin Aven' where choughs soared in the column above the tiny entrance all surrounded by deep snow.
Cavers have done quite a lot of speleo-meteorology, and that subject is quite well understood. As for mines ?
Best wishes,
D.Send.