Mine has also recently gotten less sensitive. Sometimes I wonder if I'll be able to answer. But it is a new development. I never had the problem until the last week or so.
My Droid is only a week or two old. It has never been smooth and since I'm always doing 10 things while I try to answer I never get it just right. I would love a "push a button to talk" app like HTC Touch Pro (the only good thing really about that phone ) Hmmmm.....
Check out myLock in the Market. You can set the phone to stay awake, and put it to sleep with the power button, then when you wake it up, no lockscreen. Try it, it's free... I also use AutoAnswer (another free one) and have it automatically answer only my starred contacts.
I bought Screen Suite to protect me from muting everyone (or hanging up on them!) so I don't know how I would use MyLock. I'll try the other one, though. Thanks!