Can bad EGR cause trnsmission problems?

I'm sorry but my experience indicates you are wrong. You also don't entirely understand how the EGR system works.
There IS NO EGR present at idle - no vac is applied at the EGR valve, therefore a leak will not make it idle rough. It will not run rough going down the road either because of the raised RPM's. You can verify this by disconnecting any small vacuum line and driving - the eng will run smooth enough at higher RPM's (than idle) that you wont suspect anything is wrong.
I've had experience with several failing EGR's and none made it run rough.
If the valve itself is sticking, it will result in power loss but that is rare.

allbrandauto wrote:

ScottG wrote:

allbrandauto wrote:
A egr valve that has a vacuum leak will give you rough idle when you go down the road the egr valve opens up letting exhust into the intake to get rid of a gas called nox don't think this is your problem again cat. converter can cause this but you would also have no power is it not going into high gear or is the torque converter not locking up if its the torque converter not locking up could be brake light switch

It wont always give a rough idle.
Vacuum is only applied under certain throttle conditions (not at idle) and with the throttle closed, the engine will idle perfectly unless the EGR valve is stuck open - that is the only time it will cause a rough idle and that failure mode is rare. The usual failure mode of an EGR is that the vacuum diaghram gets ruptured. Then the vavle doesn't respond properly. Then at intermediate throttle positions, you will have a vacuum leak because the ECM is trying to apply vacuum to it and it's leaking.