I have a rather well used black OM-1n which has the shutter speeds exactly 3 speeds behind the marked - for example when set to 1/4 sec I get 1 sec (compared with my trusted Pentax SP!) - 1/2, 1 and B all behave like B. The 1/1000 is more like 1/125. It seems like a fairly easy problem to fix, but I don't know how to get at the adjustment. The only reason I am bothering - I already have a very nice OM-2n- is that I replaced the seals and cleaned the body before finding the fault!
Answered my own question. Seems when I removed the lens mount ring, because there was dirt and brass dust under it, I dislodged the plastic toothed ring under it that engages the brass gear under the mirror box that selects the shutter speeds. It wasn't in correct mesh, so I was getting B at the point where it read "2" (1/2 sec) on the outer ring. A bit of trial and error re-engaged it and now it fires like it should. Tinkering again.