There is really no need for supplements when on a juice fast if you are drinking a wide variety of vegetables (including greens) and fruits. However, many people, including myself sometimes, do include the power drinks, the green drinks and so on while juice fasting.
If you still feel compelled to take a supplement, may I suggest you look into the liquid supplements as they are absorbed within the body within moments, while solid pill form takes a long time to digest and much of it is not utilized, instead it is passed through the body, so you are not getting the full spectrum of your solid pill supplement. It is said 98% of a liquid supplement is absorbed within the body within minutes of consuming. Then there is the fact that vitamin pills are petroleum based which is why they smell so bad when you open the jar. I take Body Balance by Life Force, to give you an example of what's out there.
Here's a link that talks about Body Balance and other liquid wholefoods that can be utilized on a juice fast if one believes their body needs more nutrition than the veggies, greens and fruits are giving them on their fast... http://curezone.com/blogs/m.asp?f=573&i=19
I agree with you, you are correct Livingwater... Wine, beer, or Sex on the Beach is off limits during a juice fast. There are many informative articles and books that discuss this.
The wine won't just slow down detox, it is heavily taxing the liver unecessarily while the body is in vulnerable detox mode. It's on the same level as smoking when on a juice fast, although I am sure many will disagree.
Just my two tomatoes worth,