The reversible reverser

APL, 5

⌽⍞⍝⍞⊖

This reverses (⌽, along the last axis) the input (⍞), and is followed by a comment (⍝ marks a line comment). Reversed, the program reverses (⊖, along the first axis) the input, and is followed by a comment. Because the input is always going to be one dimensional, in this case ⌽ and ⊖ are functionally equivalent. It is perhaps even sneakier than the GolfScript solution, so here's a cleaner solution (no comments), which scores 9.

⍬,⌽,⍞,⊖,⍬

This first grabs an empty vector (⍬), flattens it (monadic ,), and reverses it (⊖, along the first axis). This still leaves an empty vector. Then it concatenates (dyadic ,) to the input (⍞), leaving the input untouched. It then flattens (monadic ,) the already-flat input and reverses it (⌽, along the last axis). Then it concatenates (dyadic ,) another empty vector (⍬) to the reversed input. This does nothing, and leaves the reversed input behind. Reversed, this program does the same thing, based again on the fact that ⌽ and ⊖ are functionally equivalent with one-dimesional arguments.

You really couldn't say I'm adding useless characters to break the palindrome (the two different reverse functions are different with two-or-more-dimensional input; I'm just taking advantage of the fact they act the same with one-dimensional input)

Unix shell - 8 + 25% = 10

rev||ver

Previous answer of cat|tac didn't actually work, tac reverses the order of lines, not the order of characters in a line.

Haskell, 53

main=niam
niam=interact reverse
esrever tcaretni=main

Technically not a palindrome, but, since function declaration order doesn't matter, once reversed you have exactly the same program.