Ditto what Dunge said. I read all the time online how people use detergent in place of soap. I cringe every time.
Here's a little info I found on a quick search...
http://www.gardenmyths.com/dish-soap-damage-your-plants/
As for the mites, I am totally chemical free so when I got mites a few months back, I tried predator mites for the first time. Worked great. Never had to spray anything anywhere. I was a month into flowering so I didn't even want to use soap.
Predator mites will be they way I go from now on.
You might try spraying some fresh clean water on the leaves to wash off the detergent. Then just wait and hope.
On the other side, the new growth looks more affected than the old big leaves. Hopefully, it's not a pH problem.
Good luck and green mojo.