Congrats on 700! Good story choice. I agree with the host that it's underrated. Nice narration here, too.
A couple of thoughts:
I don't see the flaws that the host mentioned. It's a very short story that's almost a fairytale; I don't think it needs much in the way of characterization. Having said that, the host's comments about Trippetta possibly being the mastermind makes me really want to read a re-imagined version of the story.
The host also says that Poe was being lazy by simply describing the King and his ministers as being "fat." Well, on one hand, it is a "fat = evil" trope, but it misses the larger point of why he wrote them as being fat. Think back to the beginning of the story where the narrator muses on the relationship between fat and humor. He suggests that there may be something innate in the substance that breeds humor. Now, what were candles once made of? Animal fat. The description of the king and his men foreshadows the climax of the story: fat is funny and the jester's last jest is to take advantage of an abundant supply of the jolly substance.
P.S. Pseudopod may not have done a lot of Poe stories, but PodCastle has done a few. Fans should be sure to check those out. Pseudopod has done at least one Poe inspired story: episode 166 "Something There Is."