I actually know 4 professors here who wear socks with sandals.
What's supposed to be wrong with wearing socks with sandals?
There's also the possibility that they were 'dressing the part'. When doing a quick check on sandals with socks, I noticed at least one person say, "You don't want to look like a professor." If professors are 'the type of people who wear socks with sandals', then more may do so than would occur naturally.
Yesterday I attended a meetup where the discussion turned to fashion for a time (because apparently the mini-camp participants were given some instructions on fashion as a useful part of instrumental rationality). (Unfortunately none of us knew much about the topic so the discussion turned into "how can we find an expert to advise us for minimal cost?") It was mentioned that dressing "badly" can be a useful signalling device, and some examples were given. Here's an attempt at a more complete list of possible signals one might be sending by dressing "badly".
The idea here is, if you do decide to start dressing "well", know what you're giving up first. (Of course you're also giving up possibly implying that nobody taught you how to dress and you're not sufficiently strategic to have thought of learning it yourself. Or implying that you don't have the mental, financial, and/or social resources to keep up with fashion. A lot of signaling depends on what your audience already knows about you, or can infer from your other signals.) See also Yvain's related post, Why Real Men Wear Pink and comments there.