It happens on occasion that some of my family eats milchigs and some fleishigs for supper. If it’s unclear whether a pareve dish became milchig, for example, lets say it’s unclear whether one of the kids took their cheesy fork and used it put some salad onto their plate. Can one who ate fleishigs eat the salad? (Assuming of course that he doesn’t see any milchigs)
Are their other similar scenarios of doubt where the halacha would change?
The Shulchan Aruch (Y:D 89-4) says that we may not eat the leftover bread of a meat meal with milk, because the bread might have gotten some meat on it. This is also the reason why we have separate table clothes for milk and meat- because there can be residue of one type that will mix with the other type. The Aruch Hashulchan (Y:D 89-15) says that ideally salads and all other foods that were eaten with a meat meal should not be eaten with a dairy meal, because residue from one can end up on the other. In your instance, where it was not only eaten with a dairy meal, but you have reason to doubt that it might have indeed gotten milk inside of it, it shouldn’t be eaten with meat.
As a side point, this is in part why it is not a good idea for the family to be eating meat and milk on the same table, because mistakes of this kind can happen frequently.