Ok, when shifting from park to rev or 1st, it takes way too long to get in gear. I actually had one occasion where I waited about thirty seconds before it finally took. It seems like reving the engine slightly helps, or it may have just been a coincidence.

As soon as it thaws outside, I'll change the tranny fluid (I know, I know MOPAR ATF+3) filter, any adjustments that I can do that are in my Haynes manual. I'll also probably replace the relays that like to cause havok in so many people's cars.

What are the chances of this issue going away when I do that maintenance?

The trans seems to work just fine after it's finished taking its sweet time getting into first.
[>:]

 

It seems that you got it covered Oilstain.
How cold is it in your area? If it's too cold, it may take the tranny a little while to shift normally. As the tranny fluid warms up, it should shift smooth again, if it doesn't then I would suspect the fluid being out of spec....the tranny too, since it's most likely fairly old. The tranny isn't a big issue though, as long as it was treated with a little TLC, but the fluid is what's picky in this case.