Radiator Fins in Hot Water Baseboard - Basic Question
This is a frame challenge - the problem isn't so much how to fix the heating system, which I suspect will be far from a DIY job, but rather how to improve the comfort level in the apartments.
You have a identified a likely real source of the problem: the windows are very drafty so warm air leaks out/cold air leaks in faster than the heating system can heat the room.
Replacing windows is generally very expensive.
Insulating the windows is generally very inexpensive. My recommendation is something like this:

There are plenty of kits of this type available. Basically they have a plastic film, a frame (e.g., special tape that you put around the edges) of some sort and you use a hair dryer to heat-shrink the plastic to fit.
This is not a perfect solution. But it can work fairly well because (a) if positioned correctly it can cover over actual cracks (e.g., window doesn't close 100%) and (b) the dead air between the plastic and the window glass acts as an insulator. It is easily removable, so if your landlord won't pay for it then you can do it yourself and be able to remove it when you leave (not to reuse, just to avoid a damage deposit). It is clear, so you still get light through the windows.
Your landlord should be willing to pay for this, because if it gets the apartments to the point where the heat does not have to run 24/7, that will have immediate payback on the gas/electric/oil bill, in addition to providing you with a more comfortable place to live.