Here's my summary of the differences between the two versions of the game.
1. There are no bonuses for using all 7 tiles. (No Bingos)
2. The board has a different (Homer's head) shaped board.
3. First player is decided by who is closer to 'S' (for the Simpsons) ties are broken alphabetically. (R beats T)
4. There are 10 action tiles included in the game. After you use a tile, you draw a replacement tile. (The rules are vague as to whether you can use the newly drawn tile during that turn, but I interpret it as that you can use the new tile.)
Those tiles powers are:
A. Bart: Place a word in a completely different area of the board. It does not need to connect to the existing formation.
B. Cletus: Place a word that is misspelled by one letter and one letter only. (By the letter of the rules, you could use this to add a Q or a Z to any word.)
C. Grandpa: The next player after you loses their turn.
D. Otto: "Mix up everyone's tiles. Your tiles are not affected unless you want them to be." I interpret this to mean to put all the affected tiles in the middle, and everyone redraws their hands from those tiles. The player who played the tile can put their tiles in or not.
E. Ned: When your turn ends, play now goes left (counter-clockwise).
F. Skinner: If you add letters to an existing word to form a new word. (Plurals are included) you double the points for the new words. This can be added to letter or word bonuses.
G. Wiggum: Reveal one player's rack of tiles. The player affected can spin the rack as fast as they want to reveal it, but "who knows if some tiles may go flying off." (I interpret this to mean that if tiles do go flying off, they are still visible and players can look at them.
H. Burns: The next player only gets half the points on the next turn. The person who played the tile gets the other half.
I. Mr. Teeny: "If you spell a word that is only two letters, use this tile to double your score. This doubling of your points would be in addition to any extra word or letter points designated by the board." (I think this is the most vague of the tiles. I interpret this to mean that any two-letter words you spell this turn are doubled, but I could easily see this to mean that your entire score for the turn is doubled if you made a two-letter word this turn.)
J. Patty and Selma: Take an extra turn after this one.
5. There is a one-page list of bonus words. If you spell a word on the list you get additional bonus point. (Since it doesn't specifically say it, I would say these points are not doubled by word multipliers.)
5 Bonus Point Words
10 Bonus Point Words
15 Bonus Point Words
So that's about it. I hope you enjoy Simpsons Scrabble.
Let me know if you see any errors, as I'm working off of a scanned copy of the rules.