98 Grand Marquis Running Rough Occasionally

The check engine light is off, but the car does begin to run rough around 40 MPH after about 10 minutes. Very sporadic, engine will run smooth and then it will run rough.

How many miles? When were the plugs last changed? Are you having to add any coolant?

130,000 miles.
I just replaced the intake manifold and put in new plugs too. The old manifold was leaking between the manifold and the engine block. I did torque the manifold down per specifications (18 ft-lbs in the proper sequence).

This is my son’s car and he has not driven it much but I did not see any antifreeze leaking after the repair. I will monitor as he will be driving more this week.

Was the old manifold leaking coolant? You may have a COP (coil on plug) that is failing because it was shorted before when coolant leaked into the plug well. If so, the plug should also be replaced, even if it was replaced not long ago.
A Ford specific scan tool can run an engine test that would likely give you some misfire counts on the cylinder with the problem COP. Otherwise, you may be able to tell by inspection.
I’d do something about it now, before your catalytic converters are damaged too much by the misfires.

Next time it runs rough, get out on the highway where you can floor-board it and try to accelerate as hard as you can… This will usually trigger the CEL and then you can pull the codes and see what they indicate…Maybe COPS or possibly a stuck / sticking EGR valve…If any of the COPS have ever gotten wet, that’s usually the end of them…When changing a COP always replace the spark plug too…