In the movie Fight Club by David Fincher, the protagonist has Dissociative Identity Disorder. Can anyone out there give examples of how this movie accurately portrays the illness and also give some examples of how this movie makes a mockery of mental illness, only adding to the already negative stigma attached to mental illness?

Dissociative Identity Disorder (DID) used to be referred to as Multiple Personality Disorder (MPD), but was renamed when psychologists realized that DID was more accurately causing a fragment or fracture in an individual's sense of self, rather than growing secondary or new personalities (as MPD implies).
Much of the way Tyler Durden's DID is portrayed in Fight Club is largely accurate, according to the National Institute of Mental Health.
He experiences two distinct and separate identities.

The disruption in identity involves a change in sense of self, sense of agency, and changes in behavior, consciousness, memory, perception, cognition, and motor functions. ("I look like you want to look, I fuck like you want to fuck, I am smart, capable, and most importantly, I am free in all the ways that you are not.")

Frequent gaps are found in memories of personal history, including people, places, and events, for both the distant and recent past. (Edward Norton's character has either absent or inaccurate memories of Fight Club and Operation Mayhem.)

These symptoms cause clinically significant distress or impairment in social, occupational, or other important areas of functioning (this is well played out in the final confrontation between the two). 
One key difference is that Edward Norton's character did not seem to experience any significant childhood trauma, which is noted as one of the leading causes of DID. The implication here is that the culture of consumerism enacts that trauma on all American men. However, this is where the narrative philosophy of the film (and book) does start to stray from psychology. It also somewhat makes the condition seem "cool" by giving Edward Norton's character a sexy anarchist gangster as his alter-ego, possibly downplaying the remarkably difficult struggle it is to live with DID.