If you are sure it's coming out from the screwed flanged joint
between the drain pipe and the disposal body, remove the screws and
check the gasket to make sure it wasn't damaged during installation.
If the gasket looks OK, then try smearing a film of silicone caulk on
both sides of it and reinstalling it.

Thanks, I'll give that a try.

Well, your FIRST mistake was to not buy a replacement that
occupied the same "space" as the old one.

Couldn't be helped. The old one was 10+ years old and huge. The ones
they make now are smaller and more powerful.

If you don't have enough slip joints in the drain then you might
have to replace some of the drain plumbing so that the adaptor just
"slides" into place after the disposal is in place.

Not quite sure I follow. It's dripping where the water drains out of
the disposal, not where the end of the drain line meets the drain
plumbing.