For the record, mice aren't that big a deal for me; I grew up in farming town (a cousin has a huge dairy farm, my grandparents had chickens/crops) and I grew up on a lake (which is always ripe for rodents). My wife's house (before we married) was also on a lake, and now the house is unoccupied so I had a rodent problem there.
Peanut butter and mechanical traps have worked fine for me (though the best is still our four-legged feline friend).
Katt, I know it's the landlord's responsibility, especially as it's coming from a unit you do not have access to, but in the interest of your well-being and in mitigating the problem, run out and get some steel wool; it's cheap at Home Depot or Wal-mart (couple bucks). They'll chew through paper towels, they won't chew through steel wool. Stuff that in any holes/cracks you see (mice can fit in some crazy small places; if you're looking at something and saying "eh, I don't think he can fit in there"... stuff some steel wool just to be safe, because they can.