| An expression which seems to me to be true in some sense, false in some sense, and meaningless in some sense.
On the one hand, any belief which you hold firmly will tend to skew your perception of the world around you, and thus lead you to think and behave not-sanely. For instance, if you believe that members of a certain race or sex are stupid, you will tend to perceive the actions of persons of that category as stupid.
On the other hand, we use certain kinds of beliefs as necessary elements of reasoning about the world around us. You are able to form predictions on the basis of your beliefs. Provided that those predictions are not too inaccurate, you can then use them to inform your decisions and improve your life. For instance, if you believe that drinking and driving will kill you, you are less likely to drive drunk -- and even though a single DUI might not actually kill you, it's probably something to avoid.
On the gripping hand, "mental illness" is not an objective judgment of someone's ability to perceive or predict reality. It is rather a medical term referring to certain syndromes of socially aberrant thought or behavior. As such, it may be considered inadvisable to throw it around in casual banter.
lakeonfire: Well, that isn't Catch-22, but it is a bit of paradox if approached head-on. I think the resolution, though, is that most of our behavior, especially on the level of societies, is not founded firmly on fact or reason. Even our languages did not really develop to fully accurately describe the world, but rather to do a good enough job to help us survive and get on with one another.
The act of medicalizing "madness" into "mental illness" is a historical process which has happened for various reasons, some which we might personally find reasonable and some we might find wrong or even malicious. As the postmodernists would say, it is problematic.
One may attempt to state "belief is a sign of mental illness" in words which are less fraught and more likely to help us make sense of the world. Korzybski tried to do that, as part of General Semantics. | 
