I train teachers to use a cc math program and what I see pretty consistently is that many elementary teachers themselves have number sense gaps and find it difficult to teach number sense well because of that. By and large, middle school teachers don't have that issue. Also, since cc requires kids to explain their thinking, I see a huge improvement in that department on the part of the kids. Where it is implemented well, it is beautiful to watch in action in the class room. Where it is implemented poorly, it can be disaster. Often, teachers don't have time to do the self-study they need to do to get themselves up to speed to teach it well.
On the other hand, I was in a school yesterday that was doing a bang-up job, and I have never been so impressed with a public school. So the news is not all bad.
I have no idea about implementation for Common Core in anything other than math.