LED-lighting problem
The new LED style bulbs have complex power driver electronics in their bases, the brightness is controlled mainly by this internal circuit not by the socket voltage.  Putting these bulbs on a dimmer switch is like slowly reducing the supply voltage on your computer and expecting the display to dim.

Before buying an LED bulb you could check the specifications to see if it compatible with any type of dimmer switch.  Most are not. Also since LED bulbs as so new (for residential lighting) there are not yet many standards followed for their operation.  Some specialty LED bulbs are beginning to become available with dimming systems specially design for that type of bulb.  

If you had used small fluorescent bulbs in this same setup you might also see a strange operating condition.  

Standard incandescent bulbs work with simple voltage limiting or pulsed dimmer switch devices because the bulb is basically just a simple low value resistive pieces of wire. Some of these dimmer switches rely on this simple resistance and high current characteristic to create the dimming affect.  So when using the newer LED or florescent bulbs the dimmer circuit no longer sees a high current or simple resistance and the dimmer operates strangely.