After a heavy rain some of the smaller state highways or 'Farm Market' roads will have water over the road. Southwest of Amarillo more than once I have come up on roads you could not drive through right after a heavy rain storm. You won't have to worry about that with the major interstates.
Rattlesnakes are common in the outskirts of town (like around the welcome center) keep an eye out for them. They normally will not bother you if you do not bother them.