An example of this is from CCGbank (Hockenmaier, 2003), where all modifiers in noun-noun compound constructions modify the final noun (because the Penn Treebank, from which CCGbank is derived, does not contain the necessary information to obtain the correct bracketing).
there are nonnegligible, systematic errors in both the training and testing material, and the CCG parsers are being rewarded for following particular mistakes.