What are some examples of foolish behavior in Persuasion?
The novel mentions the word "foolish" particularly referring to people who make ridiculous and counter productive choices that ultimately affect their future.
Wentworth called himself a foolish man because he was about to choose a woman to marry whom he simply did not care for, yet, felt obliged to propose to. He knew that this choice would probably not be the best and he had to think it over and over. For this, he considers himself a fool. (CH 7)
One mention of Sir Walter describes him towards the end of the story as a "foolish baronet", who was considered so by Wentworth for the actions that he took and for the choices that he made which, ultimately, led them to misery and poverty squandering away his vast fortune. (CH 24)
Therefore you can conclude that being foolish is equivalent to acting without thinking.