What is a mild detergent?
I'd presume they just mean dish soap and not some more powerful cleanser.  With regard to additives, etc. I guess whatever you are okay with normally should be okay.  Obviously you have to rinse the trays thoroughly to get the soap off.

I've had a few dehydrators and there is nothing special about the plastic trays.  I doubt they are dishwasher safe but I've never put that to the test (I suspect it would not work that well anyway).  The trays can be pesky to clean if you've used a marinade. The best thing I've found for this is a small, soft circular brush.