Arrow attaches the brake fin to the car spine beam, so it is right down the center. The dogs are attached to that beam as well, with the chain dog on one side and the anti-rollback on the other. I don't know if the dogs are identical or not, but even if they are, they might not function properly if reversed...there might not be enough clearance forward of the pivot, or there may not be a required limit stop.
At Silver Dollar City, on Thunderation, they took a 6-car train and reversed cars #3 and #4 if I remember correctly. Well, Car #1 has only one hitch, so it needs to be on the front. #2 has a pair of dogs, so it has to go forward. #5 has a pair of dogs, so it has to go forward. And #6 has only one hitch and a bumper on the back, so it needs to go at the end running forward.
(Dave grabs the packet that Scott just alluded to)
It appears that the chain clutch is a symmetrical assembly with the chain dog and two safety dogs mounted on a single casting. There is a note that the part is normally installed under the back of the car, but can be installed under the front of the car as well. To run backwards, it would make the most sense to put the chain clutch backwards at the front of the car.
The only other issue I can think of with the PTC is lap bar release...but many PTC trains have electric lap bars with one busbar on each side of the train, so all it would take would be to reverse the polarity of the busbars in the station. The mechanical lap bars come in two flavors...with the side plungers, those are on both sides, so that would be no problem; the little wart mechanism, though, would be all wrong if the train were backwards.
--Dave Althoff, Jr.