A couple of my own points to add:
When it comes to seeing visible pieces of food, remember that the food may not be getting completely chewed, since this person is pretty little. That could account for whole pieces. And yes, even adults have issues digesting corn or "whole" foods like an entire berry.
If the rash WILL NOT go away, or get better and only gets worse, it may be a yeast infection. My kids got them all the time, and my little baby has had them too. I wish I knew what caused it, but the only way to get rid of it is to use an antifungal. The generic name is Clotrimazole, and you can pick it up at any pharmacy without a prescription. The tell tale signs are a rash that begins with a "pinprick" appearance. Usually in the folds or creases, or under the testes in boys. Then it takes on a "shiny" look, quickly followed by open sores.
Red all over is usually a sensitivity to either the diapers/wipes or a food. When kids are really little, I always find that some naked time, with no diapers or cream or anything is helpful. BUT, that is tougher when they are older, and I would not do it with daycare kids.
I LOVE Sudocreme. I have used the Butt Paste, and I don't think it's effective on a rash that is already there. But it's okay as a preventative barrier.