We have a 2002 Dodge 3500. The right hand turn signal flashes rapidly front and rear when in use and the left signal flashes normal.
The four ways flash normal on both sides. We replaced the turn signal switch and it still is doing the same thing.
Any suggestions as to why the difference in signal rate?

 

Sounds to me like you have a bulb out. Thats the only reason I can think of.

 

Short to a ground. Look for bare wires and such also check terminal ends. I had the same problem with the left turn, but it turned out to be a shorted turn signal switch.

 

Some manufactures lamps are more sensitive to voltage and wattage ratings. Make sure the bulbs installed are the correct rating for the vehicle.

 

yes the wattage on the bulbs can very well be it, because alot of times the circuits are very sensitive to that especially in turn signal/brake light circuits. If its a short to ground like jakebrake suggested then more than likely one of your bulbs will not be working, but from what you wrote i would assume that all the bulbs are working.

 

Dont forget to check the relays. You can switch the relay from the Right to Left side and see if the problem moves to the other side. If thats the problem $10 will fix it.

Just my $.02