I think the simple and obvious answer to this question is "Yes". That is, everyone at some point in their life is likely to make a 'big mistake'.
Regret is the likely emotion felt subsequent to making a 'big mistake' and is a well researched topic as per the references below.
There are countless situations in which an individual is likely to feel the emotion of regret, including: divorce, bankruptcy, loss of a close friend, self-inflicted injury, resigning from employment in a rage, being sentenced to jail etc. (The examples chosen here are likely to reflect instances where the big mistake endures for more than a few months.
Clinical psychology is the profession with specific training for helping individuals move on from their mistakes and overcoming a deep-set emotion of regret.