After Pesaḥ, it is better not to use the ḥametz that was sold until one can assume that the rabbi has bought it all back. When necessary one may take out some ḥametz immediately after Pesaḥ with a willingness to repay the gentile for it at his request. It is best that the rabbis stipulate explicitly with the gentile that a Jew will be obligated to pay for any sold ḥametz he takes, if the gentile so desires. Thus, there will be no question about the Jew taking ḥametz immediately after Pesaḥ.
Some people are strict and do not eat ḥametz that was sold because, according to the stringent poskim, such a sale is not legitimate, and so this ḥametz has the status of ḥametz she-avar alav ha-Pesaḥ, which one may neither eat nor derive benefit from.
In practice, however, one need not be concerned about this stringency, because the prohibition of ḥametz she-avar alav ha-Pesaḥ is rabbinic, and whenever there is uncertainty about a rabbinic law, halakha follows the lenient opinion. This is certainly true where only a small number of poskim are strict, while the overwhelming majority permit. Indeed, there were great rabbis who, after Pesaḥ, would make a point of eating ḥametz that had been sold through mekhirat ḥametz, to demonstrate that the sale was in keeping with halakha.
When shopping for food after Pesaḥ, one must make sure that the seller has a certificate verifying that he sold his ḥametz in keeping with the halakha so that one does not buy ḥametz she-avar alav ha-Pesaḥ. Even more caution is needed if the seller is not religious, because if he did not understand the significance of the sale and continued to sell ḥametz in his store during Pesaḥ, a few poskim (Sdei Ḥemed, Maharam Schick) maintain that the sale was not legitimate, and that it is forbidden to eat or derive benefit from any ḥametz in his store. In this case, it is proper to follow the stringent poskim and wait for goods produced after Pesaḥ to arrive. If, however, it becomes clear that the seller performed bedikat ḥametz in keeping with the halakha and was careful not to let anybody go near the ḥametz that was sold one may buy ḥametz from him immediately after Pesaḥ.