I have about 2300 games played in league of legends and i can tell you that because you are not using v-sync this happens. When i made this computer about 6 months ago the same thing was happening to me. I put v-sync on and i went from about 250 fps to 60 obviously but all graphical glitches stopped.
hmm, interesting. never played LoL myself so I don't know. if this fixes the OP's problem that would be awesome