Continuation of the question: Until when should one be concerned about chametz that has passed through Passover

First of all, thank you for the clear and detailed answer. From the rabbi's answer, it seems that the concern that the chametz before me (and I see that its production date is before Passover) was not sold to a non-Jew is a distant concern. This was the only concern I had... I would be happy to hear if indeed this is so, and if there is a difference between a large and important supermarket and a small kiosk. Also between a secular and a religious supermarket. Thank you very much.

Hello,

There are two issues with chametz after Passover. 

The first is that it might not have been sold. The second is that the sale might not be effective. 

In stores that have certification that their chametz was sold, there is no concern of the first issue immediately after Passover, because the chametz was in the store itself during Passover and was sold according to the law. However, specifically after some time, when chametz that was in the factory or with various agents begins to arrive, there is sometimes reason for concern. 

But the second concern, that the sale might not be effective, is always relevant. [The doubt arises from the concern that there is no complete intention to buy and sell, as well as from several doubts regarding transactions in the sale to a non-Jew].

This concern is known as the opinion of the Vilna Gaon, who was stringent not to rely on the sale of chametz in the case of complete chametz. The main stringency today stems from this concern, which is defined as a 'stringency'.