I don't know about common core specifically.

However generally I find the issue tends to be two main things.

1) They're always pushing for a one size fit's all approach. Thinking one style will work for everyone... and inevitably having a ton of people fall through the cracks as a result.

2) They focus on preparing you for something that will be 20 years old.
Essentially, they assume the world that children to grow up to be in will be the same world that they live in now. We can hardly predict what the world will be like just a few years from now let alone 20. School is going to be failing constantly if we're preparing for something that will practically non-existent when they graduate.

We'd be far better off just helping children improve in where they're strong, utilize their gifts (and some other basic life skills. Such as basic English, enough math to follow taxes and such, enough history to learn from our mistakes, enough science to not think the sun revolves around the earth or the earth is 6000 years old etc). That way everyone is trained in what they're good at which gives them a bigger chance for success than being streamlined into an outdated system they most likely don't care for regardless.