I don't think I am mentally ill at all. I live a completely normal life and I am not really hindered in any way as far as my relationship with my partner, social life, academic career or my job. Not to say that transitioning will not affect these things, but I don't think my identifying as male will change my desire to seek success. Sure, I dislike my legal name and sex marker on my IDs and legal forms, but I consider it to be a physical disorder more than anything else. For some reason, my body decided that it liked estrogen. I think of it as a hiccup in my physical development that caused undeserved amounts of stress and emotional pain. I consider mental illness to be hindering in some way, or something that requires medical treatments designed to affect the chemicals in the brain. The family and friends that I have that do suffer from mental disorders (mental retardation in development, social anxiety disorder, autism and bi-polar disorder) show signs of difficulty in daily life that I personally do not have. This is not to say that being trans is not affected by these things. A lot of trans folks have social anxiety disorder, depression and other things that is caused by the fact that their bodies do not match their minds. In my opinion, transition will bring my body more in line with my brain, which I consider physical.
However, I can see the argument for treating transgender/transsexual people as if they have a mental condition. A lot of people have difficulty wrapping their minds around someone suffering from a physical or hormone disorder if they cannot physically see something that would be considered a deformity. Saying that it is a mental condition makes some people feel more comfortable with the fact that anyone in the trans community would chose to alter a body that functions normally. I do think that having some sort of medical diagonsis is helpful for those who seek any type of medical treatment and getting that treatment covered by insurance companies.
People who seek cosmetic surgery for any number of reasons are not required to submit to a medical diagnosis. If I had gotten into a car accident and needed facial recontruction, the medical system wouldn't tell me that I had to be diagnosis with something. (For some reason the term 'facial dysphoria/identity disorder' came to mind). I don't think that the standards of what gender is under the medical system is accurate, though. Plenty of people fall outside of the two-catagory system.
But, this is only my personal opinion and I do not speak for everyone.