Ah, c'mon, John. We don't know
all the details.
I rented a "cheap" place from a "cheap" landlady once. I thought it was going to be a problem getting things done. However, I found that as soon as I offered to take care of a problem - I replaced the dishwasher, replaced a ceiling fan, repaired the A/C, etc. - she was more than willing to "reimburse" me with rent "discounts". She was very reasonable; she even took my time into account when coming up with a "discount" figure.
However, I may simply have lucked out...
Nonetheless, if avaserfi thinks it's worth it (and, sadly, I wouldn't be surprised if it's not), it couldn't hurt to get some quotes for new windows (i.e.,
all the windows in the apartment; not just in the HT room) and see if the landlord will waive a the rent for a few months in exchange for taking care of the problem for him. Win/win. Double-win for the landlord if he benefits from lower heating bills
and a tax write-off for improved insulation.
Of course, get it in writing.
Then again, maybe some folded-up cardboard shoved between the sash and the frame will solve the rattling...