I'm doing some work now with someone who has done a lot of research on schizophrenia and eye stuff, so the below information is just based on what he's told me (I haven't independently verified it myself).
There certainly seem to be retinal changes associated with schizophrenia, but no retinal test is as of yet sensitive or specific enough to be of any clinical use. However, it's important to remember that the retina is an extension of the CNS, and as such it is the easiest and least-invasively visualizable piece of the CNS. If you are doing research in schizophrenia and want to look at the CNS to assess it's health (we know schizophrenia involves problems with the CNS), the retina becomes a good target. Also, seeing retinal changes in those at high genetic risk for schizophrenia would give us some information about the pathophysiology of schizophrenia as it would suggest CNS dysfunction before the onset of symptoms.
One problem in trying to assess brain functioning in schizophrenia is that many aspects of the disorder lead those afflicted to perform worse on most tests. So if you give some sort of test to a control subject and a person with schizophrenia, and the control does better, you won't know if that's because of some specific aspect of the schizophrenia or if it's due to medications or if it's due to active hallucinations distracting the individual or if it's an issue with motivation etc. If you could design a test where the dysfunction in a schizophrenic brain caused the person to perform better than a control, you could really pin down what you're looking for. Optical illusions present just such a test as they rely on our brains to do some extra work to tell us we're seeing something we're really not seeing. And so, if you show certain optical illusions to people with schizophrenia, they're more likely to see what's actually on the page -- they don't get fooled as normal controls do -- and therefore perform better on the test.