Special inserts include parallel refractor cards of each base card that are even shinier, but with different color hues. Additionally, you can find "1 of 1" printing plates, autographed letterman cards of some rising rookies, rookie patch cards and some inserted autographs. The only Dodger insert I know of is the Clayton Kershaw Finest Moments Autographed card. See that card at the very bottom of this post.
Russell MartinClayton Kershaw Autographed Insert