The CLM doesn't currently tell BBEdit that there's anything special about inline-C blocks (C{ … }C). Ideally, syntax highlighting in those blocks should be handed off to the C language module. Doing that would require switching to a codeful language module.
As a start, these blocks should be added to the skip pattern so BBEdit won't try to parse them for functions or (if I'm reading the docs correctly) highlight them.
This in turn will require the string, function, procedure and comment definitions to be rewritten as regexen rather than defined in terms of tokens.