Are there any reasons not to mix plants in different tanks? Like say if I have a plant that's doing really well in one tank and I want to take clippings and introduce it into another tank, would that be a bad idea? I presume that if all the fish appear to be in good health than there wouldn't be any issue, but I wanted to check first.

I think it should be okay unless you have reason to believe your fish could have disease/parasites. E.g. if you've recently gotten new fish I wouldn't do this in case they could have something, but if you have had all your fish for awhile and nothing seems out of the ordinary with them than I would go ahead.

UGGHH pond snails. I tried several different varieties of non-aquatic plants in one of our tanks over the summer. I suspect the little pests came in off of one of those. I don't think they do anything bad really, they eat dead plant matter. I just find them irritating to look at. They survived a bleach dip when we transferred some of our plants to another tank. The 70% of the dipped plants didn't survive but the snails did.

So now I transfer plants between freely between invaded tanks. Plants from the clean tanks can go to invaded tanks but only plants that have been in quarantine for a month or two go into the clean tanks.