Sheldon, however, added that deals such as the insanely cheap Belize flight are exceptionally rare but said anyone can find great deals on flights. The biggest mistake people make when booking flights, according to Sheldon, is booking direct. “The main mistake people make in booking flights is going straight to the airline website. “‘Mistake fares – when thanks to a system error flights cost a fraction of what they should – are a win-win situation. The premium carriers are often more likely to honor their mistake fares than airlines at the more budget end,” he said.