Well it's a dryer for starters - so you're going to have issues with the moisture that is sucked out of the clothes, which needs to be vented to outside.
You could invest in a condenser dryer, that traps and collects the water. These can take a long time to dry clothes, and aren't very energy efficient.
You could invest more money in a condenser dryer that has a heat pump, and this is much more energy efficient. I highly recommend the Bosch one. http://www.designawards.com.au/application...licationID=8934
Do you have a ducted kit added to the dryer? It redirects the air in a concentrated format - my DH made one out of large plastic pipes and had it diverted to our bathroom, where we have the exhaust fan running.
You could buy one of these, and pick up an old door from a recycling place - you can then put a hole in the door to vent directly outside, and you won't get the cold come into the house in winter.
You can put the original door back on for inspections, and when you leave the place.
Actually, maybe you could ask the RE if the landlord is willing to put an exhaust fan in the laundry?
You could also invest in a dehumidifier - this can be used in other rooms as well.
Do you think your dryer is the cause of the mould in the other areas of the house???