1986 Cadillac Deville oil dripping

IT could be from many things. Most commonly is the drain plug is loose or the gasket on it is bad. However, it could be any of the following:

oil pan gasket
oil filter
valve cover gasket
rear main seal

What I would recommend is taking it to where you have your oil changed and let them recheck their work to make sure everything is tight. Also, while the vehicle is on the rack, if they tell you it's not leaking from where they worked on it, ask them if they can see where it is coming from and to show you. Let me know what you find out and I will explaine what needs done. NOTE: Make sure the oil is full. Based on your description, it sounds minor.

Joe

Its seems its coming from the oil pan and transmission. The mech stated that both of the pans gasket will need to be replaced. I didn't think it was the transmission leak because the color of the fluid on the ground is black. I guess he thinks they both need changing.

First, if the trans isn't in need of service and the fluid stays full and what is on the ground isn't red, you are right. There is no reason reason to change the trans gasket. Now, as far as the oil pan, how much is it leaking? Also, do you only notice the leak after an oil change or is it all the time? The reason I ask is because of the oil filter location on your vehicle. If the tech isn't careful, oil will lay on the engine and drip slowly from the pan area.

Joe