There: refers to a place whether concrete or abstract. I am going to go there.
Their: indicates possession as in "It is their right to object to this post."
They're: a contraction for they are. They're going to try to remember.
Simple enough I would think. I am not sure it is even a lack of education that causes these errors, it could just be a lack of caring. I remember as a kid having this drilled into me. Along with not using like every few words or the correct usage for here and hear.
I am starting to sound like my mother. Not sure if that is a bad thing or not, she was a History/English major in college and edited all of the newsletters and books my dad wrote for the UNR History of Medicine department. I am really not that into either subject, I just have certain things that bug me I suppose