The most significant problems with Common Core seem to be that some of the available course materials are substandard (please note I said some) because adoption of the standard was pretty abrupt, and parents just can't understand the math. See
this article from the Washington Post.
Common Core math seems to produce produce good results, but the curriculum is so different from how parents learned, that they are clueless as how to help their kids. Heck, this is and issue I've wrestled with a long time. I graduated High School in 1970, and there have been very few times in my life since then that I've needed to solve quadratic equations or use calculus in my daily life. So, helping my kids with traditional math has been a real struggle. After all my kids are 16 and 19, so do the math:)