I tried making complaints to the apartment Mgrs several times during the year(plus), their 'solution' was to (twice) bring in a lame exterminator who simply smeared some goo on the cabinet hinges and that was it.
Plus, the wifey is afraid to bring the health dept/gov't involvement into it as she's afraid of retaliation.
Then it seems as if you're gonna have to "do it urself"....If ur apartment is infested, then it's gonna take a long time to get rid of all the rodents/roaches. If you lived in a house, I've heard of spreading Boric Acid under it (crawl under the house) and block it off so animals cannot get in there. Not sure if this would work in Minnesota, tho', since it's cold there...but it works in Florida. It controls the roaches, and you can use it also in ur kitchen cabinets, along baseboards, etc. Basically, spreading it liberally around the places you see the most roaches and roach eggs.....After a few days, you will be literally sweeping the roaches up. Then again....it's a posibility that ur neighbors are not clean....so that would mean you have to upkeep this often.....But being very, very careful if you have cats or dogs....Home Depot has the gel for Roaches also (the name slips my mind)....but some people I know have used it and it worked very well....
As for rats/mice, I don't know much about that...but there are many pest control products at Home Depot you can use. And check around for any holes in the walls, (check under ur kitchen sink, also ur bathrooms), places that they can get in to ur apartment. Block them so the rodents/roaches cannot get in.
Always take ur kitchen trash out (we do every late evening)....swab down all your kitchen counter tops with Bleach! Even ur kitchen cabinets too, bathrooms, etc. If you have wood floors, mop them with a little bleach and cleaner....
Really, it seems so unfair that it's gonna cost you $$ when it's the Landlord's responsibility.....