Heim's Turrets
I've had on two occasions recently had Heim's turrets doing weird things, one game his turrets locked onto the two champs I was against in a bot game and continues to shoot them from across the map after they respawned, enough to kill them as they reached me. This stopped once I put down new turrets. The second time was last night, his turrets had insane attack speed early game, like 4 a second or possibly higher. This continued with each new turret, but appeared to slow down as the game progressed. This was a bot game also.
Can't really tell you how to replicate it because I don't know what I did, only thing different I can think of is I was trying some flat ap quints.