Two common behavioural biases witnessed in such markets are overconfidence and herd mentality.
What harm can they cause?
During a bull run, investors suffer from overconfidence bias. Since they are making money, they grow confident about their investing abilities. They don't attribute their returns to market forces but to their own skills. Their perception of risk also declines, and they take chances which they would not in saner times.
Another behavioural mistake seen in such times is herd mentality — following others blindly. The result of these biases is that investors don't want to diversify their portfolios across asset classes or even across market caps. Such biases can result into huge losses when market corrects.