Naive C++ programmers tend to use pointers as if they were references. They do not seem to understand pointer arithmetic, pointers to functions, etc. They also do not seem to have a deep understanding of memory models, and tend not to understand memory alignment. They do not use bit-wise operators much, though it's more of a cultural thing than skills issue.

I have never met a competent C++ programmer that does not have at least some exposure to C as well. But I'd dare to guess, that such character would not understand the C preprocessor in any but the most trivial level.

[edit] I originally used the phrase "C with classes" crowd, in a rather derogatory way, to describe the people who never get to learn any of the languages well, and end up writing some sort of sanitized, structured-programming, algol derivative in (a subset of) C++ syntax.

While reading the rest of the comments, I remembered that "C, with classes" can also apply to C hackers that just use C++ to structure their C-styled code, and may take advantage of a few features of the language. I have edited the comment to clarify what I meant.