I am concerned about chemical residues remaining on plates, dishes and crockery when washing up. Providing I can detect no grease or food residue when rinsing, can I be confident that no chemical currently used in most common dish detergents are able to adhere to the surfaces.
The residue on rinsed dishes is very low. I personally do not worry about it.
The main surfactants in hand dish detergents are anionic surfactants like sodium alkyl sulfates. These surfactants are known to rinse without residue from glass. Secondly, they have good safety profiles; they have been commonly used in toothpaste.
Some materials in dish wash detergents, for example automatic dish detergents, do leave an adsorbed layer by design. These include anti-spotting agents to make glassware look clean in harder water. These detergents at one time included TSP (phosphates) but now generally include custom blends of ingredients to improve cleaning and reduce streaks and spots.