I took it off yesterday so it could all dry out, and I've got duct tape gunk
all over my paint.

Is there something good to remove such stuff without damaging my paint?

Avon Skin-So-Soft...the clear kind, not the creamy kind.  It's the best for
removing tape and/or sticker gunk!    Of course, if you don't have any
on-hand, it will take a long time to get it.  In the mean time, you could try
WD40.  You want to go with something oil-based.

-Lauren