I think that the only effect that you would notice is corrosion dulling nonstainless steel. If you hand wash a carbon steel blade and don't dry it the edge may corrode appreciably. I'm with Cliff that hot water may accelerate the effect. Detergents vary in the degree that they may cause corrosion, but any hot detergent solution will strip off oil, grease and wax that might otherwise protect the edge from the water. Hot water and copper pans might set you up for galvanic corrosion. When we were making thermite out of improvised materials a friend of mine used to make ferric oxide (rust) by boiling extra-fine steel wool in a detergent solution then leaving it to soak in water with a couple of drops of bleach. The detergent stripped off the wax that comes on the steel wool and the bleach provided nice corrosive ions in the water. The air and water did the rest.
Dishwasher detergent varies in corrosiveness. The good ones at least have some additives to reduce the etching of glass and porcelain. They probably try and minimize the etching of stainless flatware. They also don't want the formulation to etch through the dishwasher housing and pipes (usually stainless). If you use a good dishwasher detergent I would only expect nonstainless blades to be significantly corroded. (But you will quickly thrash most handle finishes). You would probably see some rust spotting on the blades if you had a problem.