I'm not sure how many hear have experiences that speak to this, but I had a couple of interviews where I was first and I wonder how this might have affected my chances. People say that going first means you could set a high bar and they will compare everyone to you (but god forbid someone passes your bar) or you may fade into a fuzzy memory by the time they are done interviewing and be at disadvantage. My own experience was that SCs seemed to be a bit disorganized for my visit (some meetings fell through or weren't well attended), which I imagine they learned from/improved upon for the subsequent visits, which may have given those candidates a slight advantage.
If you're a strong candidate, order-effect shouldn't matter much. I was the first candidate a committee contacted for a phone interview using a conference call system. It took them almost half the interview time to figure out the system, leading to a fairly abrupt end to the interview. I still was invited for a campus interview. So, focus on what you can control like doing your utmost best.
Everyone always asks about this but it does NOT matter, especially because most schools only ask about 3 people to interview. I could only see this being an issue if they invite a large number, and even then I don't know which spot would be best. Last = recency effect, but also burnout and proactive interference. First = primacy, but also working out the kinks and forgetting with time. Middle = worked out the kinks and no burnout, but lost in the mix.
I do think you're at a disadvantage if you blatantly miss out on certain things like the projector doesn't work, people skip your meetings, no students are around, etc., but those usually don't correlate with interview order. It could be due to things like a snowstorm, etc.