OK, my old fridge had problems keeping things cool in summer.. in winter it worked OK at a 4 on the dial. I would recommend cleaning out any ice in the freezer if it is not a frost-free (bet it isnt) to start with. (dont hack at it, turn the fridge off, leave the door open, and if you need to speed things up stick a potfull of hot tap water in the freezer compartment evey 20 minutes - and have towels handy to deal with meltwater until the drip tray under the freezer slides out to be easily emptied) Once that is finished, putting a thermometer in is a good idea, leave the fridge closed and running for about 12 hours and then take a look at the temp. For optimum storage of most things 34-35 is good if you can get that low. Turn the temp control all the way up (max, 7, whatever) and leave a litre/quart of milk on the top shelf just below the freezer (not right at the back wall, try the middle of the shelf. If the milk gets a frost crust or ice crystals around the opening, turn the temp control down about a quarter of one division number/marking. Temp of 38 F is adequately cool. If your fridge is not maintaining enough cooling even when set to 'the max' it could be one of several things - 1) bad door seal - is the seal gasket strip torn or split? patch those defects with tape or replace the seal if you can find one. 2) compressor cylinder is worn, and not doing the job. This means replace fridge. Landlord has to do it, and no, he ought not to charge extra, if you rented with a fridge you ought to have one that works. Sue him for food poisoning due to defective equipment and he may regret not finding you a working replacement unit. (threat,threat, maybe works) 3) freon loss due to bad or worn compressor. it does happen. in this case as you do not own the fridge and such an occurrance is an EPA violation once the landlord is made aware of it (and the possible fines), it stands to reason that he/she should find you a replacement unit. Might mean someone else gets stiffed with your bum fridge at worst.
bad landlords for about ten years, I only rented the cheapest apartments I could find. That was 25 years ago, though.