Going by the exif data on the file (more properties tab in flickr) the shutter speed was 1/5th of a second, not 1/250th or 1/4000th.
You have guessed right, it looks like pronounced camera movement combined with a slow shutter.
I suspect you haven't meant to take this picture at all and have tripped the shutter whilst moving it.
A couple of pointers:
In manual mode the camera will revert to the last manual settings you used when in manual mode, no matter what mode or settings you are in when you turn the control dial. You will need to reset the exposure when you turn to Manual.
For this kind of shot you will need to use a longer exposure.
I also noticed that you have used a very high ISO of 1600. This will give you a lot of noise on the final image or print. The black sky will look very mucky rather than deep and clear.
I would set a low ISO, 400max, pref 100.
I would set the widest aperture that you can get away with, although your lens goes to f3.5 at the wide angle, you will get better quality by using f5.6 or f8.
It's then just a question of using the shutter to control the exposure.
Remember you are exposing for the light, not the for the dark. The camera will meter off the dark and try to make you over expose. You are more interested in keeping detail in the lit area I would guess. So expose for this. The EV scale may read -2EV or lower, don't worry, review the image and check that the lit area hasn't burnt out, if it has then increase the shutter some more until you get it looking right.
You should use a tripod for night shots. If you set the custom function for mirror lock up and switch on the self timer the camera will flip the mirror up then after a delay of 2 secs, will take the picture. This will avoid camera shake.
As you are using a tripod you should also switch the IS off,as the gyro will still work away otherwise, causing motion blur.
Finally, shoot RAW, for these kind of shots it gives you a lot more adjustment at the PC. Artificial light can vary wildly in colour temperature, so it gives you a bit more control.