The word "their" indicates ownership. "They're" is a contraction for "they are", showing a state of being. "There" is most commonly an adverb referring to location. Contrary to popular usage, the three words are not interchangeable. They each have a proper time and place, and those times and places are never the same.
A tangible object called a retarded has never existed. It does not currently exist; unless someone creates a play-on-words product in the future, it never will exist. Therefore, it is impossible for someone to possess a retarded. So people should stop using the phrase "their retarded".
People commonly misuse "they're" as a possessive pronoun. Perhaps it is the apostrophe; today's feeble-minded internet users can only imagine an apostrophe being used to denote ownership, thus all apostrophe-touting words indicate ownership. Nevertheless, "they're lives" does not make sense. A life is something one owns, controls, subjugates, or relinquishes. It is not something a person can actually be. Perhaps we should outlaw the contraction in common English; that might persuade people to stop relying on it in improper situations, and we can put the whole "will not" becomes "won't" problem behind us.
"There" is a referential adverb. It indicates a point (either tangible or metaphysical). Even though it can refer to a place, it cannot take the place of the previously mentioned homophones. Here is an example from a confused individual:
CORY52768 (1 minute ago) I think they're doing something constructive with there spare time. some people can learn from these two kids. (emphasis added by author)
I hope this helps in your future internetting. The great thing about the English language is that it is so dynamic; we are so capable of creating new words whenever it suits us (hell, I just used "internetting" as an intransitive verb). Therfore we should not have to bend the rules of the words we already have.
For more examples of bad grammar check out YouTube.