Originally Posted by
freestay
Or does booking one leg at a time hurt my chances for finding seats?
Booking one leg at a time won't hurt your chances for finding seats. It will double your change and cancellation fees, if you need to change both legs or cancel the trip, and it will prevent you from using the Excursionist Perk, if that's applicable for your itinerary.
If those aren't limiting factors for you, then you should absolutely book what you see when you see it. You may never see it again.
(Also: on any given route, seats may
never come open, especially if you're looking for UA-operated flights. The days of widespread award space release at T-330, at least for United flights, are long gone).