Cylinder misfire - may be something else.
 

Daughter's '98 Grand Marquis - OBDE says #3 misfire. Have changed both plug and coil, no change. Roughness most noticeable at low idle then up at the 40-50 mph range (where it's shifting up to OD?). I'd switch the OD off but the switch doesn't work - if it's a fused item, which one?

Could be a fuel injector, which you can swap with another cylinder to test, wiring to coil or fuel injector. Low compression for the affected cylinder.

The plot thickens. The OBDE changed to #8 cylinder misfire - I'd just replaced coil/plug a few weeks ago. While I was thinking about that, I cleared the OBDE. Next drive it said #4 misfire. Something is misfiring, you can feel it but the transmission tugging is perhaps the torque converter - does the '98 have a converter drain plug?

Your description of the "Cylinder Misfires" indicates that the intake manifold is leaking coolant into the spark plug holes -- most common on cylinders # 4 & 8.
1. Disconnect NEG (-) Battery Terminal.
2. Remove plug/coil wires, 1-at-a-time -- DO NOT remove the spark plugs -- THEN blow compressed air down the plug holes -- if coolant comes out, you've found the problem.
3. Need more info --
What brand and number are the spark plugs?
What brand and number are the coils ??

Holy s**t, man !!
You're older than ME !!
I thought I was the resident geezer here, but you got me by a few months.
I guess you know that we've run the course of the Mercury automobile -- first sold in the Fall of 1938, and now gone from the scene.
I restored/modified a '95 Marquis, which I plan to drive 'til I can't drive no more.
I'm in good health, and can see just fine, so the wife and I go cruising throughout the Western U.S.A. -- searching for hot mineral springs.
https://cimg2.ibsrv.net/gimg/www.mer...eae0c02c3e.jpg
'95 MERC at Flaming Gorge, Utah

Thanks for that input - will get the compressor on it ASAP. The plugs are Motorcraft AGSF32PM and the coils are Motorcraft DG-508/3WTZ-12029-AA. I hate to ask but what if I do blow liquid out of the plug holes? The intake was recently replaced by a friend - a metal water passage version.

The plot does, indeed, thicken --
About those spark plugs -- the part # that you gave is the correct part as installed at the factory. That plug is a SINGLE-PLATINUM type.
The factory shop manual (used by dealers) has an addendum that addresses these plugs.
Notation says that when replacing spark plugs, install a DOUBLE PLATINUM type for maximum longevity.
I found out about this the hard way -- plug failure after 40,000 miles -- 1,500 miles from home. The Mechanic installed a set of Denso plugs, which got me home.
I did a bunch of research, and found the ideal spark plug for MY engine -- the BOSCH Double Iridium, #9605 for my '95 MERC, and the BOSCH #9606 for your '98 and later engine. RockAuto.com has the plugs AND the best plug prices.
If water comes out when you blow down the plug holes, it means the intake manifold is leaking into them.
If you had the manifold replaced, the job may not have been done properly. Bolts MUST be tightened in a specific pattern, and an accurate Torque Wrench MUST be used. Manifold bolts MUST be brought to factory spec, and in the correct sequence, or it's all for nothing.
Hey, I gotta run -- catch ya later !!
**Chuck**