I've had some problems with my original two transplanted Fanfare cucumber plants. The pollination process has been mediocre — only one successful fruit from four female flowers — and the leaves have been dying off more and more. Though I'm told by a good friend that this is natural, I'm wary about the whiteflies that have been hiding out under these leaves. So, I'm on a quest to learn more about cucumber growing, especially for growing in containers without any direct sunlight.
As for whiteflies, here's what they advise on eHow.com: How to get rid of white flies
Soapy water. I gotta try this immediately.