It's wrong because most of the time, but certainly not
always, we have two parents. Therefore the apostrophe goes after the term
"parents" because the house belongs to the parents. It's like saying,
"I'm going to the squirrels’ hideout." If there is only one squirrel,
we can say, "the squirrel’s hideout"; otherwise, we use the plural.
Likewise for parents. If our parents are divorced,
separated, widowed or otherwise reduced from two to one, it's appropriate and
absolutely correct to write, "I went over to my parent’s house." But
chances are you're not going to say that because it's pretty formal. When
you're referring to both your mother and father, you’re likely to say,
"parents" whereas if you’re talking about one parent, you'll probably
say "my mom," "my stepmom," or "my dad." For
example, "I went to my mom's house."
One way to catch this mistake is to keyword your
manuscript or article at the end and look for the word "parent’s."
Then you can tell if the context is correct.
Sigrid Macdonald is the author of three books,
including Be Your Own Editor (http://tinyurl.com/7wnk5se),
and is both a line-by-line and a content editor for books, articles, magazines,
and essays. Visit her at http://sigridmacdonald.blogspot.com/