Newbie veggie gardner begs for help

Hi everyone. Im a first time veggie gardner trying to grow some peas, baby bush watermelons and cucumbers.
Im noticing that every so often I will come across a young leaf that looks like the top has been cut off, as in bitten off. I live in the city of Los Angeles so no wild animals here, nor any loose pet rabbits or the like in the vicinity.
Also, yesterday I proudly showing my mother in law my little starting to grow watermelon fruit, real tiny but obviously it was the beggining of some sweet melon. Today, gone off the vine as though it never was.
Is there some pest I may not be aware of that nips of young leaves as though with a scissors as well as grab the newborn fruit aside from the others already mentioned in this forum, such as deers and rabbits and the like? I have already eliminated the snail population in the area so they are not the problem.
I greatly would appreciate any help I can get to save my garden. Thank You in advance.
IB
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You might have a small worm or a grasshopper getting to your plants. I noticed the same thing on my garden plants, and sprayed them with a liquid Sevin mixture (Or a similar product found in Wal-Mart). You have to do that late in the evening so you wont kill any of the pollinators that come visiting.
Dwayne

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