Thank you for your question to eXtension.

Most people will tie the large (healthy) leaves over the top of their cauliflower to keep the curds white.  This is called "blanching." I don't think I'd do that with dying, diseased leaves, though.  So go ahead and trim any leaves that are yellow or brown.

The caterpillars are one of a couple of species of cabbageworms that attack all members of the cauliflower family.  They are easily controlled with a treatment of Bt, which is a naturally occurring bacteria sold by the trade name Dipel.  It kills only caterpillars, and is safe for humans and other beneficials.  You can also use Sevin (carbaryl) or Malathion, but these will have a harvest restriction which will make you wait 1 or more days before harvesting.  Be sure to read and follow all label directions. 

Please let us know if you have any other questions.