Here's a look at some premium Dodgers-related memorabilia that are currently available at Love of the Game Auctions -- the most notable item being the 1959 Gold Glove Award that was given to first baseman Gil Hodges (seen on right). (Auction Link) Apparently, this is the first time this item has ever appeared on auction.
The oddest and most unique item is the below vintage board game produced by Kamm Games Inc. in 1947. (Auction Link) It is called "Casey on the Mound" and it featured Dodgers star righty Hugh Casey.
As you can see below, you are meant to stick your hands through the little window; which strikes me a very unwieldy.