There are two broad ways where a minority can show up in a movie with a positive effect towards breaking down stereotypes. There is, of course, tons of bad ways (or maybe just one) where a minority might show up in film to negative effect, or to reinforce stereotypes. That is actually a much more complicated discussion compared to this one.
1) Just Showin Up
This is the worst way to portray a minority without having a strong negative effect. This is also what I think you might call the "Token" effect, where somehow it just reminds audiences that people different from themselves might exist. I hesitate to even call this a positive effect, but I suppose in the end it is, because it exposes audiences to those that might be different from themselves. And while that's not really the most beneficial way to use the medium of film for a mass audience, hey, it's better than nothing.
The character's difference is never really acknowledged throughout the show, and they are merely a replacement for the role that any actor could play. When this is done right, however, it can reinforce our lack of differences between ourselves. Take
But that was a character with depth and uniqueness. A sight sadly not seen often enough.
2) But, you're a girl!
I'm trying so hard to put a positive spin on all of these and it just gets harder and harder. The second way that a movie might raise the awareness levels of its audience is by bringing in a character to subvert a character's (and, by extension, an audience's) stereotypes about the group the minority belongs to. A few quick examples of this would be the "ass-kicking, tough-as-hell female" and the "prissy jock".
When this works poorly, it can be lame and obvious. Think about movie that come out now where the main character has to pretend to be gay, and that's meant to be funny. That maaaaaay have worked several decades ago, but we're at the point in American culture where unless you're out of your fucking mind, there's nothing weird about this.
It can also work to reinforce the stereotype it was supposedly trying to break down, whether inadvertently or...advertently. Think about a few romantic comedies where the main female lead starts out as an independent career oriented woman, and then regresses into a relationship-obsessed girl. Or perhaps if the movie draws so much attention the character's differences with the rest of the cast, it does more to segregate than anything else, not mention reinforcing how weird it is when minorities don't fit our preconceived notions.
For this to work well, the joke must be played on the audience. I think the best example of this is in Paranorman. Throughout the movie, the young teenager character is constantly throwing herself at the football star quarterback character and keeps getting shot down. At the very end of the movie, where it's revealed that the quarterback is gay, it is the audience's fault for never making that assumption. The evidence was there the entire time, you just chose not to see it.