Well, as an example of something that has always bugged me - an invisible man will always be blind. This is because light passes right through him, and therefore there will be no image formed on his retinas.
I suppose it's possible to postulate that he only allows visible wavelengths to pass through him, but is opaque to some non-visible parts of the spectrum, *plus* his retinal photochemistry is uniquely adapted to be sensitive to those non-visible parts of the spectrum (The X-men series has examples of mutants with "synergistic" powers manifesting together, e.g. Viper in the movie Wolverine, who is not only able to secrete her own venom, but is also immune to all known toxins). But this also offers an easy countermeasure for enemies using special optical equipment to hunt him down. Of course, the other alternative is that the invisible man can 'see' by echolocation a la the movie version of Daredevil (who is blind but very much visible).