We've added 6 leaderboards that track top scores in the community for the 3 Arcade worlds. When you complete all the puzzles in an Arcade world, the best time to win each puzzle is added up, as well as the total moves remaining when the puzzle is won. You can replay the puzzle as many times as you want to try and beat your best time or moves score. This will then update the total score for the world's leaderboard.
A good strategy is to use the Bounty Bonus to collect extra moves and that way you end up with more moves left when the goal is achieved. You'll probably play a little differently, depending on whether you're going for best time or using fewest moves.