Any theory of information needs to comply with what we call the implementation, formalization, and representation constraints. These constraints are justified by basic considerations concerning scientific modelling and methodology. In the first part of this paper, we argue that the implementation and formalization constraints cannot be satisfied because the relation between Shannon information and IIT must be clarified. In the second part of the paper, we focus on the representation constraint. We argue that IIT cannot succeed in satisfying this constraint for semantic contents without offering models for concepts, conceptual roles, and context sensitivity. In the final part of the paper, further complications are raised with respect to the distinction between consciousness and attention, which apply more specifically to the representation constraint. We conclude with some recommendations as to how IIT may succeed in solving these problems, highlighting the advantages and enormous potential of IIT as a scientific theory.