Calling this a thinly veiled take on Hitler isn't quite accurate. Chaplin's Adenoid Hynkel is, directly, Hitler by another name. Just as Napaloni (Dictator of Bacteria) is exactly Musolini. Garbitsch was Joseph Goebbels, and Herring was Hermann Goering.
Chaplin's first proper talkie (his earlier works were sound films, but performed in pantomime), The Great Dictator is both a slapstick comedy and melodrama. The slapstick parts are amusing and quite interesting. We see remnants of the tramp character (retired with Modern Times) as well as notes of the Marx Brothers and Stooges, the big difference being that Chaplin's character is polite and understated.
The change in tone from slapstick to melodrama was jarringly abrupt, making me wonder if Chaplin was undecided which path to take. But when Nazi expansion in Europe is a current event, goofy is a hard sell.
Hollywood did not want this film made and Chaplin had to finance it himself. Why anger a ruthless dictator by calling him out for what he was? Also, the Jewish studio moguls didn't want to call attention to their Jewishness. Considering the climate at the time, this was a very brave act dared by few.
The Great Dictator is a well made, sometimes funny, but important film. It is quoted and referenced more often than you may think. It came out a full year before To Be or Not To Be, which I may give a slight edge to (it certainly balanced the humor element better). and was beat by the Stooge short You Nazty Spy! by less than two months. Consider the years this production required compared to the super tight schedule of a Stooge short.
Chaplin was disappointed that his movie didn't get more respect at the academy awards, nominated five times with no wins. But it could be worse. His hot wife could leave him and marry the Penguin. AMRU 4.
In lieu of a quote, I leave you with a modified version of Chaplin's speech at the finale. Maybe it's a bit of a spoiler, but it's truly inspiring, especially in light of recent events.