On my Let's Play World, I am unable to attack mobs with my fist or items (exception is tools such as swords, axes, pickaxes, shovels, etc).

My world was created in 0.12.0 alpha. I believe any worlds created before 0.13.0 was affected. I can certainly say that most worlds created in 0.12.0 alpha was affected and you cannot attack with fist. Any worlds created in 0.14 alpha builds are not affected.