The term "politically correct" is often used in a negative context, but politically correct terms are ultimately about showing respect to people by referring to them in the way they would like to be referred to. Determining the politically correct terms for mentally handicapped folks can be challenging, since retard, idiot, moron and many other terms used in the past to refer to mental handicaps were also used as insults. Demonstrate your old-school values of respect and propriety by using politically correct language.
In certain contexts, mentally retarded is an appropriate term. Mentally retarded refers to someone with an IQ at or below 70, a poor ability to adapt and an onset of the condition before the age of 18. In many cases, however, this term is not preferred as it doesn't include people who suffered brain damage later in life or have specific sorts of mental handicaps such as aphasia. It also the source of the pejorative word "retard," and as such can be hurtful. Using the word accurately and in the appropriate social context determines whether it will be seen as politically correct.
Developmentally disabled is a good alternative to mentally retarded, since it is not linked to any pejorative terms. It also covers conditions like autism and cerebral palsy which don't necessarily involve a low IQ. Like mentally retarded, however, it only covers people who have an early life condition that leads to mental handicap. A person who, for example, got into a car accident and sustained head trauma is not developmentally disabled.
"Challenged" has become a preferred word to "handicapped" and mentally challenged is a politically correct catch all for people with mental disabilities. Other terms such as mentally handicapped or mentally disadvantaged also have their supporters, and no word perfectly describes everyone with a mental disability, but mentally challenged is nearly always a respectful and politically correct general term.
Name of the Condition
If you know the name of the condition a particular mentally handicapped person faces, using that term is politically correct. Down's syndrome, autism, Williams syndrome, aphasia and other conditions have distinguishing characteristics that affect mental functioning in different ways. Demonstrating your awareness of this by using the proper term for a particular condition shows a respectful and politically correct attitude.