If one mistakenly cooked on Pesaḥ in a ḥametz pot that was not kashered, if 24 hours have not elapsed since ḥametz was last cooked in the kli, the dish is forbidden on Pesaḥ and must be destroyed. If 24 hours have passed, the dish is kosher be-di’avad, as there is a rule that anything that imparts foul taste does not render a food forbidden, and after 24 hours, the flavor absorbed in and stuck to the kli has become foul. Consequently, the taste of the foul ḥametz does not render the dish forbidden (SA 447:10, YD 103:5).
If the one who cooked in a ḥametz pot on Pesaḥ knew that it had not been kashered but transgressed and cooked in it on Pesaḥ, then even if 24 hours have passed since ḥametz was cooked in it, since he transgressed and cooked in a ḥametz pot that was not kashered, the Sages penalize him and render the cooked food forbidden to him and to anyone for whom he cooked. However, others, for whom he did not intend to cook, may eat from it, since in fact there is no ḥametz flavor that renders it forbidden.
Others are stringent, maintaining that even if one accidentally cooked on Pesaḥ in a ḥametz pot, even if 24 hours have passed since ḥametz was cooked in it, the dish is forbidden, because ḥametz on Pesaḥ is treated more stringently than other prohibitions, and just as even the tiniest quantity of ḥametz renders a mixture forbidden, so too, even its befouled taste renders a mixture forbidden (Rema; above, 7:5, n. 5).
This is the status of earthen and wooden kelim even today, and this is also the status of glass and metal kelim that were not cleaned with soap, as generally accepted. However, as explained in Peninei Halakha: Kashrut 32:4-8, unlike earthen and wooden kelim, metal and glass kelim do not absorb flavor into their very substance. Consequently, if they were cleaned with soap, as generally accepted today, they do not impart flavor. Therefore, be-di’avad, if one accidentally cooked in a clean ḥametz pot, even within 24 hours, the dish is kosher. Nevertheless, there is still an obligation to kasher it (ibid. 7), so if one took a pot that was used to cook ḥametz within the past 24 hours and purposefully cooks Pesaḥ food in it, even though no flavor that would render it forbidden was imparted into the dish, due to the Sages’ penalty, the dish is forbidden to the cook and to anyone on whose behalf he cooked the dish (Rashba, Ritva, Radbaz, Knesset Ha-gedola, Pri Megadim, and others, as explained in Peninei Halakha: Kashrut 32:3, n. 3, toward the end).