Off the top of my head, using only the minimal length examples:
dad, deed, did, dud
eke, ere, eve, ewe, eye
pap, pep, pip, pop, pup
tat, tit, tot
And, of course, there is one Scrabble-legal letter combination that is two letters long and a palindrome: AA. A'a (pronounced /ah ah/) is a type of lava, which is thicker and more viscous than other types. It is characterized by flowing in a sporadic fashion and leaving a rough surface when it cools.
And if it's not already been suggested, then I propose a variation of Appletters called Palindrominoes: The word snake is formed as in regular Appleletters, but if you can form a palindrome where the base letter (the "head" of the snake, I suppose) is inside the palindrome, then you are permitted to position letters both above and below the end-tile, as shown in the example below:
eThen you can give the snake multiple heads, like a hydra or a planarian or something. A little extra chaos to spice up your Appletters game.