How tenants can suddenly one day find mould everywhere is beyond me. As soon as mould appears, it should be dealt with by cleaning with an appropriate mould cleaner or a strong solution of bleach. This is especially so in bathrooms and around windows. It is recommended to open windows for a few hours daily to help alleviate the problem. However, in my opinion and from experience, a lack of a constant warm room temperature is one of the main factors to prevent mould growth. If walls are allowed to get cold then any moisture in warm air will condense on these cold surfaces and mould starts to grow.
I fear we're going a bit off-topic (happy to discuss on another thread) ... Trying to steer it slightly back - in relation to mould, heating systems and rent... I agree with you re: warmth being needed to guard against mould, but how many landlords will give tenants credit against rent in winter months if they are having to run an inefficient expensive heating system to accomplish this?