I recently purchased a 2002 S-Type, 4.0 L with an automatic transmission. It has 100K KM (60K Miles).

Ever since I bought it, it stumbles when slowly accelerating between 1500 and 2100 RPM.
It feels like it is misfiring.
If I accelerate hard, the revs easily go past this rev range and the engine doesn't stumble.
When the revs get below that range, and I accelerate in 5th, I will get the stumble.
The engine runs fine when not in that 1500 to 2100 rev range both below and above that range.
The car sat for a while, so I ran a can of STP through the system. I am using Premium gas.
I just completed a 3,000 Km (2000 Mi) trip with the car. No issues, except for the stumbling.
My gas comsumption was 9.5L/100Km (25 MPG).

Any thoughts as to where to start looking?

 

Chances are a bad coil or an air leak.

Coil testers are available. It's very cheap to check for air leaks using such as elm327. Lots of threads you can read.