Idle surges about 300 RPMs up and down while moving.
 

This is a 2002 Audi A4 1.8T Auto.

The car idles fine even when the transmission is enganged, howerver, when I start moving the car shakes a bit and when the transmission changes gear it shakes again.

I also noticed that once the car is moving the RPM go up and down in a range of about 300 RPMs, during this time the car holds back and then continues.

As you can see this sounds like two different problems, I look forward to read ideas about these two problems.

Thanks in advance.

sounds a little like limp mode. Use a code reader to check for codes.

Shane I cleared the codes this morning, there is no check engine light at this point.

But there were codes this morning? What did they say?

There was one code, misfire cylinder 3.

This is because the coil on cylinder 3 was not working at all, the coil was replaced and the code cleared.

Ok. Vacuum leaks can cause idle issues so I would start with that and hope that fixes it.

On the shifting probs check your snub, motor, and trans mounts.

My idle is fine, once the car starts moving the RPMs start to surge; this happens when I am already moving, for example: I am driving on D at 40mph, here the RPM start to surge in a range of about 300 RPMs, up and down continously.

shane excuse my ignorance, what is the snub mount?

The snub mount is a motor mount on the bottom front of the motor.

So you can be cruising down the highway and the rpm will just be moving up and down?

Exactly! The range is pretty small though, for example: 5000 to 5300rpms.

You can can feel it and if you look at the tach you will see the needle jumping up and down.