Replacing a standard 2-gang light switch with an electric dimmer switch
As mentioned in the linked questions (see the above comments) switches that are designed to only work with incandescent bulbs frequently send a low voltage through the bulb when the switch is in the off position. This is to power some component in the switch, like a night light, a motion sensor, or the receiver for a remote control. With newer energy saving bulbs like CFL's and LED's, this low voltage will cause the light to flicker, while it would have gone unnoticed with an incandescent.

The solution is to get a switch that's designed to work with energy efficient bulbs. This switch is either a standard manual switch, or it can have a dedicated neutral connection to send power over for the switch's components. To wire a switch with a dedicated neutral, either the power source needs to go through the switch's junction box, so you can pigtail off the neutral, or if the power source comes from the light fixture, you need a 3 wire connection from the fixture to the switch (hot, switched, neutral).