The vinegar alone should suffice. http://www.hort.purdue.edu/ext/vinegar.html
White vinegar is acetic acid while apple vinegar is malic and acetic acid. Malic acid is found in many fruits as well as apples, of which the latin word is malum, hence, malic acid.
I would not add salt to any soil I expected to grow, well, anything. Firstly, table salt is NaCl which dissolves to Na+ and Cl-. Cl is fairly toxic on its own (main ingredient in chlorine bleach), luckily, being an anion (minus sign), it washes from the soil with rain rather easily. The bigger problem would be the Na, which would displace Ca++, Mg++, K+, which are essential to plants. Once Na has been introduced, your problem will be how to get rid of it since it adsorbs to soil colloids just like other cations you want to keep.
The detergent simply breaks the surface tension of water allowing it to penetrate soil easier. Possibly it stops the vinegar from beading on the leaf surface like water on a waxed car, again, for penetration purposes.