The Danza: In one episode, King Chad is dating an Emotionless Girl named Janice, who is voiced by Janice Kawaye (who also voices Ami). Of course, the REAL Janice is a pretty nice lady, according to the producers.
Screwed by the Network: A fourth season was planned to air, but Cartoon Network suddenly cancelled this show in October 2006, most likely due to a management shakeup. As a result, it didn't air the rest of the show's third season, removed it from the schedule, and took every trace of it from the network's website; they never even acknowledged the show's existence from then until October 2012, when the main characters appeared in the network's 20th anniversary poster◊.
Too Soon: The episode "Tsunami Yumi" was never aired because of the then recent Indian Ocean Tsunami.
The real Puffy Ami Yumi appeared in an awareness ad for the tsunami.