For instance, a couple of years ago, United was trying to match Southwest fares. By mistake, somebody set Southwest's one-way fares as United's roundtrip prices.
"So for a full part of the day, they were selling tickets at half price," Seaney said.
United quickly caught the error and fixed the fares but not before thousands of tickets were sold, all of which Seaney said the airline honored.
One New Year's Eve, Air Canada was switching over its Website and for a brief time was offering tickets for zero dollars.
"There's been a variety of things that occurred," Seaney said.
Perhaps the best deal of them all came from Italian airline Alitalia. Seaney recalls the airline was trying to offer unrestricted business class tickets from Toronto to Cyprus for $3,300. Thanks to a mistake, tickets were sold for $33.
But it gets better, the tickets allowed long layovers. Some savvy travelers got to fly business class to Rome or Milan on the way to or from Cyprus.
Alitalia started canceling the tickets but then people complained to Orbitz, where they bought the tickets. The airline started re-booking tickets but messed up the tickets so much that they had to allow one free change for everybody.
Delta once forgot to add the fuel surcharge on round trip fares, Seaney said, making roundtrip travel to Europe extremely cheap.
Airlines realize the problems pretty quickly and try to fix it as soon as they can. With domestic airfare, the prices can only be changed in computers three times daily.
"If they have a problem at 8 p.m., they can't fix it until 10 a.m. the next morning," Seaney said. It's even better for travelers on weekends, when the domestic prices only update once, 5 p.m. ET. International fares can be updated hourly.
To take advantage of the deals, follow blogs like Leff's or the popular FlyerTalk forum, where these deals are often found in the mileage run section. Seaney also suggests keeping track of Twitter feeds.
Several travel sites offer nightly or weekly deal alerts, but Seaney said as soon as his computer system at FareCompare.com identifies an anomaly, it automatically emails out an alert to subscribers.
"In order to take advantage of mistakes," he said, "it has to be in real time because they are fleeting."