The Halachic principle of "Noten Ta’am Li’fgam" establishes that we may disregard the taste of forbidden food that is imparted in kosher food, if it is a foul taste. Normally, if a small amount of forbidden food mixes with permissible food, imparting taste, the entire mixture is forbidden. However, if the flavor imparted by the forbidden product is a foul taste, it does not impact the permissible food, and the food remains permissible.
An example of this Halacha is a utensil in which non-kosher food had been cooked. If one then cooks kosher food in this utensil, the food is forbidden, because the taste of the non-kosher food is embedded in the walls of the utensil, and is then imparted into the kosher food during the cooking process. However, if one cooks kosher food in this utensil 24 hours or more after the utensil had been used for non-kosher food, then the food is permissible. After 24 hours have passed, the taste embedded in the walls of the utensil is presumed to be "Pagum" (foul), and it therefore does not Halachically affect the kosher food cooked in the utensil thereafter. Although one should not knowingly use this utensil, if one mistakenly used it, the food he cooks is permissible, as long as at least 24 hours had passed since the pot had last been used for non-kosher food.
The Shulhan Aruch (Orah Haim 447:10) rules that this Halacha applies to Pesah, as well. This means that if one mistakenly cooked rice (which is permissible for Sepharadim on Pesah), for example, in a pot on Pesach, and after the rice was cooked, he realized that the pot was taken from the Hametz closet, the rice is nevertheless permissible. Since 24 hours had passed since the pot had been used with Hametz, the flavor of the Hametz in the pot can be disregarded. The Mishna Berura (Rav Yisrael Meir Kagan of Radin, 1839-1933) explains that one might have assumed that the prohibition of Hametz on Pesah differs from other instances of forbidden food, because it is "Oser Be’mashehu" – it forbids a mixture in any amount. Meaning, even if a tiny morsel of Hametz mixes with other food, and its proportion in the mixture is so small that its taste is not discernible at all, the entire mixture is nevertheless forbidden. One might have assumed, then, then even a foul taste of Hametz forbids a mixture on Pesah. However, the Shulhan Aruch maintains that a taste which is "Pagum" is not forbidden at all, and therefore it has no effect whatsoever on the food into which it is imparted.
The Rama (Rav Moshe Isserles of Cracow, 1530-1572) notes that some authorities disagreed with this ruling, and maintained that the rule of "Noten Ta’am Li’fgam" does not apply to the prohibition of Hametz on Pesach. According to these Poskim, since the principle of Bittul (the "nullification" of a minority component of a mixture) does not apply to the Hametz prohibition, even a taste of Hametz which is "Pagum" renders a mixture forbidden. The Rama writes that this was the accepted practice in Ashkenazic communities, and this is, indeed, Ashkenazic custom even today.
Sepharadim, however, follow the ruling of the Shulhan Aruch, and permit food which was mistakenly cooked in a Hametz pot, as long as at least 24 hours had passed since the pot had last been used with Hametz. (The Mishna Berura writes that in communities with no established custom in this regard, one who follows the stringent view is worthy of blessing, though those who wish may be lenient.)
Summary: According to Sephardic practice, if one mistakenly cooked food on Pesah in a Hametz pot, the food is nevertheless permissible for consumption on Pesah, as long as at least 24 hours had passed since the pot had last been used with Hametz. Of course, one should not knowingly use such a pot on Pesah, but if this was done mistakenly, the food may be eaten.
