I've left my old Nashbar Townies on the bike (folded) while shopping and also taken them inside. Put them in the cart and fill them up so that I don't "over shop". I let the checker bag into their plastic bags (I reuse them around the house or recycle them), then those bags and the panniers all go in the cart to make the line go faster. Sometimes I'll repack before mounting the panniers, but the mounting system is the cheap J-hook, so I usually put the empty pannier(s) on first, then load them.
To the OP, you might want to replace the mounting hardware. I've heard good things about Arkel and Ortlieb mounting systems and I know that Arkel sells theirs as a "retrofit kit".
http://www.arkel-od.com/us/all-categ...ook-kit-1.html