I think it would be cool to have kill replays
http://imgur.com/PZjhWbf
Like just a 5-10 second replay of the kill, like a kill cam in call of duty, just click on the red dot where it happened, and you can review the kill to see if you made any mistakes, it would be quick and easy. The replays would get deleted after that game has reached the bottom of the match history list so Riot doesn't have to buy a jupiter sized amount of land for an off shore hard drive.