Haskell
This was fun and (fairly) easy! Off-by-one errors are a likely source of bugs here.
import Control.Monad
import Data.List
import Data.List.Split
import Data.Maybe
score d pat = ((100 *) <$> search pat) `mplus` search (transpose pat)
where
search pat' = find ((d ==) . rdiff pat') [1 .. length pat' - 1]
rdiff pat' i =
let (a, b) = splitAt i pat'
in length $ filter (uncurry (/=)) $ zip (concat $ reverse a) (concat b)
main = do
input <- splitOn [""] . lines <$> readFile "input13"
let go d = print . sum . map (fromJust . score d) $ input
go 0
go 1
Line-seconds score: 0.102
π