The neem oil that I applied to a couple of my chile plants last week does seem to be working. I had shaded the plants after spraying because I was afraid of leafburn. While the plants were shaded it didn't seem like the neem was working - there were still a lot of aphids. After a few days I let the plants sit in the full sun again and then I started to notice that the aphid population decreased until it seems there are very few left now. It seems that I need to be more patient. I sprayed a couple more plants a few days ago and didn't shade them - so far it seems to be OK - the plants don't seem to be suffering and the aphids are decreasing. I've also noticed a number of aphid mummies so it seems that the parasitic wasps aren't being knocked down.
Neem has also been quite effective at keeping powdery mildew under control on the zucchini plants. I noticed over a month ago that spots were developing on the tops of the leaves and the bottoms of some leaves were heavily infected. Typically, in this cool moist evening climate, once powdery mildew sets in the infection spreads rapidly and squash plants can completely succumb in a matter of weeks. I started spraying with neem about once a week and the plants are holding up surprisingly well.