This can be used when referring to someone who is a douche, asshole, dumb ass or are full of themselves. More specifically, some who can't keep their damn mouth shut!
"Wow! I can't believe you told them that! You pulled a Dirty Richardson, douche bag!"
"Did you really just do that!? You're such a Dirty Richardson!"
Doing your job so well others slack off and you get to do theirs.
Now doing 4 things at the same time and getting yelled at because you are now taking too long. Then get yelled at because nothing is now getting done.
Then get told you never do anything.
Never getting a raise while everyone else gets promoted.
To be "Beautiful, Dirty Rich" is to go out partying looking your most glamorous and having a great time not matter how much money you have (or do not have, as the case may be)
Girl: Hey, check out that girl over there, She looks amazing and has been here every night this week. She must be loaded.
Dude: Actually I heard that she's broke, but she's "Beautiful, Dirty Rich"
Girl: Oh!