Another interesting variation between styles is in which direction naihanchi starts. Some teachers teach this kata stepping left first and some stepping right first. Each style seems to have a preference, but even within a given style, occasionally you will see a teacher that teaches this thing backwards with respect to the other teachers in the same style.
It doesn't really matter (much) because this kata is perfectly symmetric - all the movements that are done on one side are repeated on the other. But it is an interesting phenomenon.
My isshinryu instructor once told me a tale that might be apocryphal but it gives what is at least a plausible explanation. According to this story, back in the olden days the teacher would teach naihanchi to one student at a time, standing directly in front of each other and close together, so that the instructor acted as a mirror to the student. Thus, every generation of karateka ended up learning this thing on the opposite side from their instructor. And whether or not that is true, it's not a bad way to teach the thing.
[photo courtesy of Mike Oliveri]