Hello,
I have a 1997 Ford Thunderbird 4.6L V8 with the standard 4-speed 4R70W automatic transmission. I just bought the car and it has a total of 51,800 miles on it. The day after I bought it I had the ATF filter and fluid changed. Big O Tires used Valvoline Maxlife ATF. My previous car was also a '97 TBird; they used the same ATF and it worked out fine.

The ATF fluid has the correct level, color, and smell. On a level surface when I am on the road and I release the accelerator, the car slows by a bit too much, almost as though the brakes are being slightly applied. When I am coasting or at a full stop and I press the accelerator, there is a slight, split second pause, then the car accelerates. When I am stopped and in Drive, the engine runs slightly rough and the transmission makes a slight turning noise. In Park, the engine runs smoothly.

My previous '97 TBird did not do this. Can someone tell me what the problem is? I am not a mechanic and have little expertise for this car. Is it a solenoid, a vacuum sensor, a low grade misfire for my 4.6L V8, or something else?

 

This is a bit confusing to differentiate what the problem is from the post. Is this an engine performance problem or a transmission problem?
Some problems are hard to parse apart, so let's see if this helps.
Does the problem occur if the gas is pressed in Park/neutral? Does it hesitate? If put into manual 2 or 1, does it change? Is it reproducable at certain load, temperatures, driving conditions? Has it gotten worse either at all or recently? Can you ask the previous owners about any history?
Usually (but certainly NOT always), trans problems are fairly reproducable, and they get worse over time. This can be helpful.
Please let us know.