I doubt they'll cancel it. It's not so low that it's obviously a mistake, as it would be if the flights were $37-40 RT instead of $370-400. It's in a reasonable range for a promotional fare. That means you can require them to honor it, as all the others who jumped on it - some of whom are, undoubtedly, lawyers. If UA tried to invalidate those tickets, which they may not want to do at all, they'd find themselves on the losing end of a short court battle with lots of attendant negative publicity. And they know this.

A while ago UA offered a real mistake fare: about $1200 round trip in business class, LAX or SFO to New Zealand via Sydney. (Someone had left a zero off the end.) It was up for a weekend during May 2007. My wife and I jumped on it. UA's position then, and keep in mind that this fare was so low as to be an obvious mistake, was "we'll honor the ticket exactly as sold; we won't allow any changes; and we'll refund it in full, because it was sold as a refundable fare." That seemed fair enough to us and to others we discussed it with. We ended up having to cancel, for reasons that don't matter here, but a good friend of ours and two of his buddies enjoyed a great Kiwi vacation on the cheap. There's been some turnover in UA management since then, but I think they'd be at least as accommodating as this with a fare that is not an obvious mistake.