Newbie, sorry if this is long but I don't know how to reply to your questions in 25 words or less.

If your bldg's had no monthly extermination in over a year, I think that's the first thing you should focus on. Find a good exterm company, decide the level of bldg service you need and include service to apts that request it on a sign-up sheet. If a company wants your business, they may give you extras and negotiate on price. Sealing holes/cracks is critical to keep mice out and you likely have more than you did a year ago. Mice are nibblers. They can chew thru wood, plaster, vinyl, and slip through a hole as small as a dime. You should also get sweeps (barrier strips) for bottom of doors for all bldg rooms (boiler compactor, pump, storage) and doors to the outside. Get metal sweeps. Mice can chew through even the hardest rubber.

Most proprietary leases say shareholders are responsible for keeping the apt interior clean and in good repair. Our attorneys say that includes sealing holes/cracks around pipe/gas lines coming into an apt, in baseboards, etc. Have your attorney check your lease. Exterms find areas that need sealing but shareholders have to empty cabinets and move major appliances. Exterms I've dealt with wouldn't do that. They also don't seal holes/cracks, just locate them.
As I understand it, if any work beyond the scope of service covered in a contract with an exterm company is requested, the coop pays for it in bldg areas and shareholders pay for it in apts. Ask the exterms and your coop attorney. Also, look through Habitat's article archives. You can also type keyword "mice" on the Net and find a lot of info on their habits, food-search patterns, how to get rid of them, etc.

Re: mice, you said "certain apts have more problems than others for no known reason." There HAS to be a reason and it's most likely holes/cracks. It could even be a split in a hardwood floor or a "mistake" hole you made in a wall to hang something and never plastered up.

Mice forage fairly close to their nest, usually not more than 10-25 feet, and they're always looking for food or water. If they find even a tiny hole they explore, and if there's food left out, open boxes of food, food scraps in trash cans, etc. in an apt, you're going to have uninvited (and unwelcome) guests for dinner.

I can't tell you too much on the warrant of habitability. It mostly referred to rentals and gets complex with coops. The standard meaning referred to a tenant being deprived of essential functions to which he/she is reasonaby entitled, such as heat, plumbing, electricity, absence of mold or lead paint. A breach of the warrant depends on the extent of the problem, if it affects health and what, if any, corrective measure have been taken. Not sure where, but I read somewhere that a coop proprietary lease has been deemed to be no different than other (rental) leases and "Courts found that a landlord-tenant relationship is created by the proprietary lease thereby rendering the coop corporation liable for breach of the warranty." (I found that in my notes from our dealings with mice last year.)

Again, it would be wise to consult your coop attorney. I'm not an attorney so don't hold me to anything legal-ish I may have written here. :-) I hope some of this helps you.