2004 Acura TL 235k miles
It takes a while (2-4 sec) for the car to shift from (P)Park to (D)Drive. After the initial change of gears the car runs perfectly normal.
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I'm in no way an expert on either Acura nor Automatic gearbox service. But in one episode of wheeler dealers they had a problem with an automatic Porsche Boxster, it was a "tiptronic" gearbox which didn't shift correctly in automatic, but in manual. He changed the gearbox oil, and everything was ok.
Since it's goes away after the initial change I thought that it might be the same on yours (like once the oil has gotten some temperature or whatever, it just works better).
But that's more of a suggestion than an answer.
Like Markus, I am not an expert but from watching countless hours of automative shows and repair videos, I could say it is probably clogged up and needs and oil change, possible cleaning. While you are at it you are better off cleaning the inside of the engine off the oil gunk build up.
235k miles is a lot for any machine, and if it has not regularly maintained and fluids changed on time, it could and possibly would have a lot of wear and tear and lots of gunk build up.
Try adding high quality oil first, and if that does not solve your problem, do a complete fluids change, since it would be time.
The first port of call for sluggish automatic gearboxes is to change the ATF, it's the simplest and cheapest task to do and, unless you put the wrong oil in or the wrong amount, you can't make anything worse by doing it. If that doesn't fix the problem, changing the oil filter in the gearbox (if it has one) would be the next thing to try.
If the changing the oil and filter doesn't fix the gearbox there's likely to be a hydraulic leak inside it and you're probably best seeking professional help unless you've done a lot of work on cars yourself; there's a reason why automatic transmission repair is a specialism within car repair.