Mismatch or non-isomorphic mapping between form and function is prevalent in natural languages. English is no exception in this respect. It displays various instances of mismatch phenomena that can be classified into two main groups: complexity and content mismatch. This paper discusses several instances of these two types of mismatch in English and sketches how the lexicalist grammar with parallel architecture can license such non-isomorphic relations or no direct correspondences between form and meaning.