Oh god. Literally, random, and could care less are my biggest pet peeves.
Literally means the statement should be interpreted exactly as written (i.e., "I literally jumped out a window.") It should never be used to indicate emphasis (i.e., "It was so awesome, my head literally exploded!")
Random, as previously stated, means an outcome reached through pure chance (such as the formation of the universe), NOT acting like a moron (i.e., "I'm wearing underwear on my head! How random!!!11 Please pay attention to me!")
"Couldn't care less" indicates that the person's level of caring is at absolute zero, and caring any less would be a physical impossibility. "Could care less" means that the person does indeed care, and is certainly capable of caring less, but chooses not to, thank you very much. This is most likely not the intended effect.