Hi, I got the dead cylinder going: #3 was not firing, and there was no spark when I laid an old plug on the cam cover and started the engine. I checked the resistance and got about 16K.
Anyway I was tired of waiting: the idle was steady, but for the dead #3 and it did not die, so I backed it out of the drive and went down the street. Right after it shifted into 2nd I felt the dead cylinder come in, heard the exhaust note smooth out, and from then on it was OK. I drove about 1/2 mile and turned around; when I parked in the drive, it idled OK; no more dead cylinder, but still not as smooth as I expected, but I have no experience with how these engines should idle.
Sounds like there may be something to that "Italian tune-up".
Oh, well, the water pump drips some, so I'll order one.

 

Idle smoothness on all teh S3 6 cyl i have been involved with has always been very good.

Many things come to play, as with any engine:

Spark plugs, gapped correctly
Timing, and all the associated components
Tappet clearances
Vac leaks, or lack of
Engine breather system
Fuel "pot" trim in the ECU
Cam chain timing, mainly the top chain.
Ignition coil integrity, along with all the LT wires.
HT leads including the coil lead.
Correct operating temperature.
Fuel quality

The list goes on, and any/many of them just slightly off the boil will have an affect on idle etc.

 

Car sat for the better part of 2 years; getting a little exercise is apparently helping it as it keeps getting better. I drove it to town 5 miles to get some gas and it ran good and idles ok, did not stall, etc.
No doubt injectors are less than perfect, for example. I may get a matched set and try that.
Thanks for the advice.

 

If your car was sitting for a couple years I very strongly suggest you check the fuel filter, ESPECIALLLY before you install new injectors. It would be such a bummer if you paid for injectors and installed them just to turn around and gum them up with sludgy or rusty fuel =|

The fuel filter is located in the trunk on the passenger side in the spare tire compartment towards the back. (not the back of the car, the back of the trunk)

Remove the fuel filter and pour the contents into a clear glass container, and look for any signs of rust or gunk.

Hopefully it all checks out good, but if not you will have more to deal with than injectors. While you have the filter out you might as well replace it with a new one, unless the tanks are rusty, you will have to deal with that first. Best of luck to you.

 

Yes, I have a new filter although there has been less than 1000 miles on the old one.
I also removed the bungs and flushed out the tanks, and replaced the suction screens.
Thanks a bunch!