I recognize that, in this economy, emphasis should be placed properly on getting an interview for a job. But as someone who has participated on the "other side of the table" for more than a hundred academic and non-academic interviews, I think occasionally about candidate sequence. Does one candidate get an advantage by going first? Last? In the middle? Often, the sequence is random; often, the sequence is determined by necessity: who is available at what time. But if a candidate has a choice, what should that candidate do? I am sure that human resource professionals have their views. Here are mine.
How about going first? The obvious advantage here is that if you make an excellent impression, you color the whole proceedings to your benefit. But if the process is a lengthy one -- I have, for example, seen searches interrupted by Christmas or Easter -- there is the danger of your impression fading. Academic searches in some departments may be uncommon events, and colleagues unaccustomed to the procedures might be a little uncertain. I am beginning from the assumption that everyone benefits from everyone being as sharp as possible. If committee members take some time to focus their questions, it is possible that they will remember the response to the best version of their question -- not necessarily the best response.
How about the middle? If the early candidate or candidates did not do well, there is the opportunity for middle candidates to drive them from contention altogether. Middle candidates get a process without bugs, and there is little chance that the committee has made up its mind, prematurely. But there can still be a lot of time between this performance and a decision, and while I am not a psychologist I get the sense that a first or last impression can be stronger.
How about last? There is always the danger that people have already made up their minds or that a committee is fatigued by this point, especially if the process has been long and involved. But I have a personal affection for this slot because of the sheer number of times I have seen a discouraged committee re-energized by a strong final performance. At the very least, we could agree that candidates at or near the end of the process have the opportunity for the last word.
Most often, I have seen the interview give applicants the opportunity to reinforce what is good on a resume and correct what might be confusing. Gaffes can always sink a candidacy, and sequence has nothing to do with that. But sequence must be important to some people: why else do some organizations try to interview all candidates concurrently?