Its subject matter (movie gangsters) is a parody of Warner's famous cycle of crime films starring such actors as James Cagney, Humphrey Bogart, George Raft, and Edward G. Robinson. The lead character here is in fact a caricature of the last named, and the title derives from the studio's own 1938 acclaimed feature film, Angels with Dirty Faces, which starred the first two. It is directed by Tex Avery, and, similar to his later MGM crime/detective-oriented cartoon, Who Killed Who?, the ostensible plot—in this case, gangster Killer Diller goes on a bank-robbing spree and the police attempt to apprehend him—is secondary to a fast and furious series of gags.
Trivia and Production Notes
The blackboard writing punishment Killer Diller receives at the end of the cartoon would later be popularized by The Simpsons as a running gag during its opening sequence.
First color cartoon to open with "WARNER BROS. Presents" in a banner on the original opening titles. But since the original titles were cut for Blue Ribbon reissues, it has not been seen on modern releases (even when restored for DVD in 2005).
This short was re-released as a "Blue Ribbon Merrie Melodies" short, deleting the specific production credits. However, on eBay in 2007 there were about 40 Tex Avery title cards for sale, many long believed lost due to these reissues, and one of them was from Thugs with Dirty Mugs, so it does survive. This came too little too late, as the short had already been refurbished for DVD release in 2005.
Censorship and Bans
The WB airing of this cartoon cut the part where one of the robbers hits a bank teller (who taunts them with "I'm going to tell-ell!") during one of their heists. Also cut was the police chief yelling "Take that, you rat!" and then feeding cheese to an actual rodent. 
According to Canadian animation historian Gene Walz, this short was banned from being released in Winnipeg, Manitoba back in the 1930s for glorifying criminal behavior and showing Killer Diller being punished like a schoolkid (by being shown in prison writing "I've been a naughty boy" several times on a blackboard with a prison-striped dunce cap on his head) rather than an adult, which the censors thought wasn't "sincere."