Can I pick a lock on a shop "closed for inventory"?

Yes, you can open the door using lock picks, credit cards, skeleton keys or the knock spell without angering the shopkeeper.

Basically any way to open the door that does not destroy it (like e.g. kicking it in or smashing it with a pick-axe) is allowed.

You're also allowed to teleport or phase into the shop if you have that ability. When teleporting or phasing out of the shop, make sure you pay first or the shopkeeper will call the Keystone Kops.

If you're routinely kicking down doors, shops "closed for inventory" might be a problem. You can carry an axe around instead of kicking -- applying it never chops down a shop door, and therefore never angers the shopkeeper.