Hi @jeremyclark13-- I'm sorry about those troubles, but thank you for the report. The issue isn't exactly that it's not escaping apostrophes... the issue is that the keyword algorithm isn't working *at all* and using the full body text as the list of keywords. I tried to use the YARPP debug mode (?yarpp_debug=1) to see exactly what keywords are being pulled out, but couldn't as you're using WP-SuperCache...
Are you having trouble with 2.6.3? All my current installs are 2.6.3 and are working fine... I'll have to get my 2.7 beta back up and test it there, but that may take a few days.
In the mean time, for a quick fix, I would recommend you turn off "consider body" and "consider title" in the "relatedness" options in the YARPP settings pane, as this will at least cut out that illegal SQL. I'll try to look into this with a 2.7 install in the next couple days.
Thanks again--
mitcho