Work in grammar induction should help shed light on the amount of syntactic structure that is discoverable from raw word or tag sequences. But since most current grammar induction algorithms produce unlabeled dependencies, it is difficult to analyze what types of constructions these algorithms can or cannot capture, and, therefore, to identify where additional supervision may be necessary. This paper provides an in-depth analysis of the errors made by unsupervised CCG parsers by evaluating them against the labeled dependencies in CCGbank, hinting at new research directions necessary for progress in grammar induction.