A major starting point to look at the misrepresentation of people of colour is certainly old-fashioned British comedies such as Love Thy Neighbour, Till Death Us Do Part and On The Buses.
While it would be a stretch to describe Love Thy Neighbour as anti-racist, its intention was somewhat decent, but it was the execution that was at fault. For 1972, when the program first aired, was an era when the average man or woman was having to come to terms with the social effects of immigration, and this led to simmering tension which exploded into violence. The Notting Hill race riots of 1958 were still fresh in the public’s mind, and tensions in often deprived areas continued throughout the Seventies and Eighties.
The intended reading was reasonable — a bigot, Eddie Booth, and his more liberal wife Joan, have a pair of West Indian immigrants, Bill and Barbie Reynolds, move in next door and the two men clash. Unfortunately, the jokes are repetitive, and the way that Eddie Booth delivers his lines when he spouts his bigoted insults about “Sambo” and “King Kong”, that suggests that he, like the audience, is supposed to find racial abuse naturally funny.
All of this could be linked to Gilroy’s Postcolonialism Theory as the ethnic group of Love Thy Neighbour are in ways dehumanized and “othered.”
Thankfully, views towards race have changed for the better. In recent years, the lack of diversity in Hollywood has become a relevant issue: in 2015, the presence of only one person of colour in the nominated actors for the Oscars had triggered a wave of anger, followed by the creation of #OscarsSoWhite on Twitter. Although being a problem known for a very long time and inherited from centuries of racism and (real or symbolic) segregation, people have finally seemed to come face to face with the issue for the first time.
In the last two years, more than half of the biggest hits in box-office has been films with a diverse cast, or people of colour as the main leads. Including Get Out, Black Panther, Crazy Rich Asian or Hidden Figures. The success of these films has shown that it was, in fact, possible to have a film that is both inclusive in terms of representation of America’s diversity (both in ethnicity, sexual orientation and gender) and successfully profitable. For this reason, many representatives of the people are hopeful about inclusiveness in the future.
Love Thy Neighbour is probably used up & down the country by Media Studies teachers as an example of a representation of ethnicity that (thankfully) you just don't see anymore. It's interesting that you also mentioned Till Death Us Do Part, as this was another text whereby the intention of the show was to satirise old fashioned bigoted views through the main character, Alf Garnett. Unfortunately a large proportion of the audience were sympathetic Garnett's struggle with a changing, more tolerant society, and as a result the show itself is viewed as problematic in its representations - perhaps that makes it more interesting as a case study for Stuart Hall's Encoding/Decoding model!?
As for the recent Hollywood blockbusters that champion…