"Dim" was a 21st century slang term for inhabitants of the United States of America's Sanctuary Districts. "Dims" were usually people with mental health problems. Grady was classed as a dim in the 2020s.
In 2024, while Benjamin Sisko and Julian Bashir were stranded in the past, they were processed into the San Francisco Sanctuary District by Lee who noted that though their paperwork labeled them as dims they didn't strike her as such. (DS9: "Past Tense, Part I", "Past Tense, Part II")
As Dr. Bashir noted with disgust, many of the dims in Sanctuary District A had psychological ailments which were easily treatable or controllable even with medicines available in the 2020s, yet because the dims were destitute, they simply could not afford these vital treatments. He pointed out that one derelict suffering from untreated schizophrenia could easily be living a fully functional and productive life, if society outside the Sanctuary District simply cared enough about providing him with basic medical care, or the employment needed to obtain it himself.