I wish people would post their solutions when they solve their own problems, so others with similar problems can see the fix.
At any rate, I'll post some possible fixes here, for others who happen to have the same question and come here.
The problem is it seems you're manually selecting vertices, and using the Weight control to manually set the weight. I recommend, if going that route, to also select a few vertices beyond (using the "Grow" control in the same section where you toggle "Select Vertices"), and pressing the "Blend" button a few times.
Alternately, you can use the Paint Weights control. It gives you a lot less control, but it allows for a lot easier and fasting application of envelope weights, which is great for just cranking out a rough rig, to be fine-tuned later.