The slide assembly dropping down slightly on an UNCOCKED 870 is entirely normal.
The Express finish isn't as rust resistant as you might want, but there are several ways to enhance it's protection.
One method is to coat all exposed surfaces with a good non-automotive wax.
Many people use ordinary Johnson's Paste Wood Floor Wax.
You can usually get this at Wal-mart, grocery stores, and hardware stores.
Just rub a coat into the rough finish, heat it with a hair dryer until it melts, allow to cool, then wipe off any excess.
Many duck hunters use this method to protect their guns in salt water duck blinds.
Another method, is the one Remington recommends for their Police guns.
Disassemble the gun, including the magazine.
Spray everything, inside and out dripping wet with Rem-Oil or, even better, with CLP Breakfree.
Allow to soak in for 20 minutes or so then wipe it down.
The Teflon and rust proofing additives will soak into the rough finish and protect it quite well.