Speaking of which, a friend of mine recently posted to facebook that he'd finally succeeded, with help, in finding a sentence where they're, there, and their would all work, albeit with slightly different meanings.
Find the kids, the dogs, and [they're/there/their] toast!
Does "there" work there? I'm not sure it does.
I could see how "there" would work. It's not conventional, but I believe you can use "there noun" in a way similar to "that noun." Although, I cannot say that without thinking of Young Frankenstein. "There castle!"
I'm not so convinced on "they're." If you use that, then the sentence becomes awkward. If you drop the second part of the compound sentence, then you're left with, "Find the kids, the dogs." As two objects, that just doesn't work.
On the other hand, if the kids were actually dogs, then that's valid. Perhaps if it were reworded to say, "Find my children, the dogs, and they're toast." From that point of view, it's not really more valid than "the kids, the dogs," but it does become something that is likely to be said.
Or better yet, maybe you're talking to your children. "Find the dogs, my children, and they're toast."
Using "there" is a bit shaky, but if you can accept sentences like, "I'm going to sit in this here chair" (and maybe you don't), then I could see "there" being used in such a way.
Interesting little bit on this here:
http://www.grammarphobia.com/blog/2012/06/this-here.html