For what it's worth, I was able to fix this problem in my circumstance (Moto DROID).
I believe the lag time in answering the phone was due to my rooting and underclocking. I had the DROID set up to run at a fixed 250 MHz when the screen was off to save battery life (via profiles in SetCPU). Since the screen is off when the phone call first comes in, the phone has to operate at 250 MHz while handling the phone call, waking up, turning on the screen, disabling screen lock, etc. All that is a lot for an underclocked machine, and as a result I didn't even see the answer slider until 1-3 rings in, and after that it was dicey as to whether I'd get it to slide in time to get the call.
The solution in my case was to disable that profile, so that the phone does not run at a fixed 250 MHz when the screen is off. My phone still has underclocking on demand, so most of the time I'm still running at 250 MHz and saving battery life, I'm just not ~forcing~ it to anymore.
The result is snappy call answering with no auto answer or screen lock apps! For even more improvement, lower the SetCPU UP threshold. But be careful - set it too low and you'll start burning some serious battery.
Hope that helps someone,
--scotto
Original Motorola Droid
FRG22 Stock Froyo Build, Rooted