When turning from a stop, my 2002 explorer has an occasional vibration / shudder that I can "feel". It does not affect handling and I only notice it from a stop and not while driving. I am not noticing any abnormal tire wear on the front tires. My dealer and my regular mechanic have not been able to find any problems. It is very slight and only lasts for a few seconds until the wheels are straightened out.
Any help?

Does your Explore have 4X4? If yes, that's probably what you are feeling and that is normal. When going very slow and you're turning the steering wheel, the tires do not turn at the same rate and the "computer" thinks that the tires are slipping and will engage the 4X4. Normal for a "Auto 4X4".