I'm too lazy to check, but in case no one's mentioned it....
I just saw The Princess and the Frog. These are things I picked up on:
1. Dr. John sings one of the opening numbers. Dr. John is the inspiration for Dr. Teeth.
2. *inhales* Naveen is one big Kermit reference. He plays a real banjo as a human and plays an improvised banjo in a swamp as a frog. He makes friends with an alligator. He has a dream. His choices of love interests are a diva-ish pink-skinned, blonde-haired, pink dress-wearing princess wanna-be and an unassuming, dark-skinned, light blue dress-wearing (at John Goodman's dance where Tiana kisses Frog Naveen) girl. This hearkens to the Piggy vs Mousey problem in TMS. Plus, there are the lovely night scenes under starry skies as everyone, including Naveen, ponders upon how to solve the problem.
3. The Frog Prince, the Muppet version, has Taminella disguise herself to get into the royal family. While Facilier doesn't do this, he DOES get Lawrence to disguise himself to get the quote-unquote royal money and possibly the entire city of New Orleans. Not wanting to spoil too much, but part of the spell of Facilier's must be LITERALLY broken, just as Taminella's spell had to be broken LITERALLY. Also, the wedding in both is attended by both people and animals. Naveen might also be a nod to Robin the Brave, who was rather sure of himself before the frog part.
4. I doubt this is a reference/homage/parallel, but to me, Mama Odie was the Marjory the Trash Heap of this movie. Both talk to the relevant prince about getting not what is wanted, but what is needed. Both have powerful magic but don't really get around much. Both have similar styles of "helping": sing a song about something slightly ambiguous and let the listeners figure out what to do themselves. Mama Odie also shakes herself during her song like Marjory does (sorry, couldn't help but notice). Mama Odie wears dark circular glasses and Marjory has black quote-unquote "eyes" that are basically just holes in her head. Both have animal helpers.
edit: And Mama Odie loves gumbo and Marjory loves Goombah.