There is a fundamental question regarding the laws of kashrut on Pesaḥ: What is the status of foods that are not normally made with ḥametz all year round? Are they kosher for Pesaḥ as they are, without any special supervision, or must we consider the possibility that they were somehow mixed with ḥametz and should not be eaten on Pesaḥ?
According to Shulḥan Arukh, as long as there is no real concern that some ḥametz fell into this food or that it has absorbed the taste of ḥametz by being cooked in a pot in which ḥametz was cooked recently, there is no need to suspect that the food contains ḥametz.
However, Rema writes that Ashkenazic custom is preferably to avoid eating specific products without special supervision for Pesaḥ. This is because ḥametz is used throughout the year, and we are not generally cautious about it, so we suspect that some of it may have fallen unnoticed into these particular foods. We are also concerned that the foods may have been unwittingly cooked in ḥametz pots.
In practice, all kashrut organizations today tend to follow the stringent ruling of Rema and do not certify foods for Pesaḥ unless due caution to avoid ḥametz was exercised during the food’s preparation. Perhaps this is the way one must act today even according to Shulḥan Arukh, because all industrially produced foods contain a variety of ingredients, and there is concern that one of them is not kosher for Pesaḥ. Therefore, during Pesaḥ, one must be careful not to eat any factory food products that are not certified kosher for Pesaḥ.
Where the facts of a case are not in doubt, there are still often practical differences between the rulings of Shulḥan Arukh and Rema. Although fundamentally the law accords with Shulḥan Arukh, the tendency today is to be stringent so that food will be kosher for all communities. This is the appropriate practice when it is not overly difficult to be stringent. However, when stringency causes significant loss, there are grounds to encourage those who follow Shulḥan Arukh and the majority of poskim to continue following their practice.
There is another concern that one cooked the food in ḥametz utensils, and it absorbed some of the ḥametz taste from the kelim. However, those who are lenient hold that there is no reason to suspect this, since it is assumed that most kelim have not been used within 24 hours and would then not influence the taste of the dish in a positive way (and would not make the dish prohibited). Furthermore, even if the kelim had been used within 24 hours of cooking the dish, ḥametz before Pesaḥ is permissible, thus the cooked dish is a “nat bar nat” (the pot absorbed the taste of the ḥametz and in turn, passed the taste on to the cooked dish) of permissible food, which is permitted; and see Yeḥaveh Da’at 1, 11 and in the notes. This fundamental dispute hinges on other issues, such as whether sharp food (davar ḥarif) restores and improves the taste absorbed in the kelim. (See Peninei Halakha: Kashrut 23:8, 12; MB on SA 447:5.)