Hi there, 
The first thing you can do is block the leaks of cold air by using large scotch tape to scotch them. It is obviously not a very classy way to do it but it does the trick for sure. 

The other thing is to put thick long and wide curtains to the doors and windows and to make sure to close them before the nightfall. 

Finally, buy an electric heater. It's cheap and it will help bring the temperature up.
Hope it works for you as it did for me,

Use duck tape to seal the clear plastic over the window.
Or you could just use duck tape directly on the window seals.
Duck tape will fix any problem.

There are many different ways to resolve that problem, which is by the way, very common here in China.  Of course, the better the solution, the more money it will cost you, even if it is a do-it-yourself.
You can beging by getting one of those "poly-plastic" tubes of sealant and cover all the seals on the windows.  I will caution you, two or three successive thin applications (next one after previous one dries) will work better than one big thick blub.
After that, if your window edge frame (the one touching the concrete wall) is wood or aluminum, measure the length and width and buy either plastic or glass, and mount it on the inside to create a so called "double window".  Make sure you seal it while mounting it.  You could also better the set up by adding some "insulator" between both pannels of glass if necessary.  Please, bear in mind that my suggestion should go forward for as long as your problem is not resolved, there is no need to do it all if not necessary for your needs.

Also bear in mind, 2011 winter is still young, wait until late January or February, then you will see that concrete walls will also be cold as hell.

Electrical heaters are cheap to buy, but expensive to run.  It costed me 1800 Rmb to run mine for a two month period, a lot more that what I paid for the heater( 760 Rmb).

My solution has been to become used to colder temperatures inside the apartment, wear sweater or jacket inside.  But at bedtime, I paid 230 Rmb for a 180 cm x 170 cm electrical blanket with dual controls, and I do sleep like a baby and very warm for a reasonable expenditure.

And yes, as the Dude said, duck tape does work in many more places than intended when developed, I also keep a roll always around

Hello, Tang Peter! I had that problem before and we decided to move out after the lease was up. There are a number of things in which you can do to avoid this problem if your gonna decide to stay in that apartment.
My best options for you would be to get an electric warm blanket the one where you plug in and it heats up. You can get a hot bag. Not sure if you have heard of these this was new to me when I first came to China as well and I'm not sure how long you have been here. Use more blankets. 
You can get a mini heater those can be costly. 
As far as the cracks your trying to avoid you can try the alternative and use something thick to cover those up. I did see that you used thick blankets you can try using towels as well. If that doesn't work keep asking people particularly in your apartment building, and ask them how they have handled that problem because if your having that problem than more than likely there are others that have that same problem in your apartment building as well. 
Here is a list: An electric warm blanket, an electric mini heater, more thick blankets and a hotbag.

Had the same problem told my landlady was fixed within 2 weeks....good luck keep warm  the coldest is yet to come

Buy a pair of extra thick pajamas.  As a bonus, they are quite stylish when worn outdoors

You can buy sports (snow) quality thermal underwear. The problem is they will get too hot!!!!!!!

use a candle and go by the doors and windows to check for drafts. Hang old blankets over the windows at night. And over the doors (after you fix all the leaks. There is this cheap V-shaped seal that you can use for where the door shuts...for little cracks as it compresses flat where needed.

Sort out the plastic leaks and use tape to seal them. Then drop 500 kuai on one of those space heaters, not a cheap one that blows air, one of the radiatior style ones. 

Get yourself a girl in the summer give her the flick, and head back out on the town.

This is a common problem throughout China simply because almost every building is made of concrete and 99.99% of apartments/offices are NOT insulated and only have single pane (cheap) windows.  Apartment kitchens are extremely notorious for this.

Duct tape is always a nice touch for helping to seal off windows, but here are a few more hints that will help keep your apartment warm in the winter:

1.  Check your AC units.  Every single one I have seen here in China has a drainage tube/pipe that basically goes through a big hole in the side of your apartment.  This is equivelent of leaving a window open.  Seal that off!  Pack in something for insulation then duct tape it shut. (this also helps in the summer to keep cold air IN)

1b.)  CLEAN YOUR AC UNITS!  Especially in Beijing or Shanghai - these things get so dirty...  Open it up, clean out the filter and also (if needed) most larger stores sell AC cleaner for the heating/cooling elements which you might need if it hasn't been done for a while.  This will save you money in the long term, as the AC will run more efficiently.

2.  If you have tile or wood floors, buy some throw rugs to cover up  the more common areas.  This is a relatively cheap thing to do, plus it makes the apartment look nice as well.  The rugs will act as at least a bit of insulation.

3.  Most bathrooms here in China have floor drains similar to those found in the bathtub/shower (or if you have the "multi-use" bathroom that doubles as a shower).  These are also giant holes which go directly outside.  Close your bathroom door when not in use, or cover that hole!  I use a bathroom floor mat to cover mine when I don't need it.  It's not a major thing, but every little bit helps.

4.  Even if you seal your windows with duct tape, get some curtains or blinds.  They're not that expensive and add another layer of insulation.  Also, in some areas, you can find sheeting used for greenhouses.  If your lucky enough to find this, cover your windows in this.  It really really helps.

5.  Your walls are probably made of concrete.  When it's cold out, your walls will be cold and suck the heat right out of your apartment.  If you can repaint, slap on a few layers of good quality latex paint.  While that's a bit of an expensive option here, it helps.  If you can't paint or don't want to, try to cover as much wall space with artwork. 

6.  Other than those options, get some warm underwear and some good sweaters!  Dress warm!

Hope this helps!

I have spent winters in Shenyang and it has always been warm inside. Is there no central heating in apartments in Beijing? In Shenyang every apartment I have been in either have the bar type hot water filled ones on the wall in every room or the much more efficient under floor heating. All that needs to be done then is block up any drafts and it is very cosy inside.
In the older style apartment I stay in, even though it is privately owned, a whole bunch of workers just rocked up one day and covered the whole building and all others in the vicinity with Styrofoam and render and then repainted it. No cost or permission given they just did it. Has made the building even warmer inside.