I forgot to rename the school when applying my SOP to another school. How bad is this?
As a long time graduate program director, I've read thousands of these essays; this mistake happens in maybe 1 in 50 or so. I have already seen one this year, for example.

Here's the deal: If it's a generic statement of purpose that is not tailored to the school in question, yeah, it hurts a bit. It's an added signal that you're not all that serious about this particular school. If your statement of purpose is well tailored to the program -- or if you've created other contacts there, e.g., talked extensively with a faculty member interested in recruiting you -- the harm should be minimal.