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Sounds like you are in an apartment? If so, see if you can have the building supervisor or owner do something to improve the door, as it IS their responsibility.
Otherwise, it sounds like your main issues are drafts, light, and insulation value of the glass itself.
Bubble wrap does do a good job of increasing the R-value of glass, while still allowing light to come through. I am not sure of the lighting of your place, but my old apartment was very dark, and I wouldn't have covered a single window there, just to make sure I got some daylight!
The big thing is just to seal up cracks any way you can! Foam, caulk, fiberglass,old socks. Just make sure it's something that will keep out moisture too, so maybe not the socks...
A 2" thick sheet of extruded polystyrene foam costs around $20. It would be around R-10, is easily shaped, and easy to decorate. You can pin cloth right to it to make it look nice. I wouldn't be a bad idea to cover the exterior side of it either, so your neighbors don't have to take a look at that big pink sheet of foam all the time.
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