Is it safe for my baby to sleep in his car seat during the night?

As long as it's reclined a bit so his head won't flop foward you should be fine. Be sure it's on the floor though and not somewhere that would risk being knocked off or turned over by a pet or a jolt. We kept our baby in a bouncy seat/binet (Eddie Bauer) for the first month because she just slept so much better. :)