I use soap on my mash tun.
The same sponge wipes the kettle that I oxiclean soaked so I would imagine soap gets in there too.
I soap my funnel, my large stirring spoon, various plastic parts (mostly different varieties of hoses), my thermometer, and possibly a few other things that I'm forgetting.
I oxiclean my kegs and all of their parts and fittings; however, my soap sponge wipes the inside lips of the opening of the kegs.
I occasionally soap my beer glasses as well, but 90% of the time I just use hot water to rinse them out.
The main thing is to rinse very well. I make sure that everything is completely rinsed, and then I rinse again for good measure. It doesn't take me a lot of time to do this. I have been doing it this way and typical beers always have a lasting head until the pint is gone. I'll post a pic later tonight when I pour myself a beer.
I should disclose that I use soap that is meant for washing baby stuff. Not sure if this makes a difference but I have no head retention problems so I continue to use it.