I've talked to a few people, and they try to "limit" the consumption of processed foods on passover, although when they "need to", as with grape juice and wine etc, they will buy it from the store. This just seems ridiculous to me: if you're anyway buying some things, why not enjoy Yom Tov with more processed foods? And what's wrong with processed foods anyway? (This is even the case when they have multiple "kosher for passover" hechtshers on on it!) Is there any source for this law?
It says (in the name if the arizal I think) that one who does not eat chametz on Pesach will be protected from sinning the whole year. (That a person will be protected from shogeg you can still sin if you choose to.) So if one only eats food that he saw from start to finish the chances of eating chometz is greatly reduced. And since chometz is an issur mashehu it's very easy to transgress an true it would be batul before Pesach but do you want to rely on bitul and even if you do there is a machlokes rishonim if bitul simply causes the whole food to be mutar or if it actually causes the issur to become heter (there are halachik ramifications) (like on shabbos if pikuach nefesh pushes off the issur or makes it mutar) so according to the opinion that only makes it mutar it would still be better (if one has good reason) not to eat it. And it has become customary in many communities to be very strict on Pesach for these reasons and in commercial processing it's very hard to keep all the chumros. Also there is a custom not to eat out of the house and certainly that includes a factory. In addition some people feel that it a a good idea because it makes people aware of the severity of the issur and of kashrut in general.