"Under his watchful and steady eye, the cashier checked out customers and gave a sleepy, half-assed sales pitch for the hats, t-shirts, sauces, and seasonings for sale in the display case next to her."

Does it mean the cashier is leering at customers?
It would mean the cashier took the payments from the customers.
But, when a guy "checks out" a girl, it usually means something evil.
Students: We have free audio pronunciation exercises.
What you have mentioned is the slang usage of 'check out' which is definitely not the case here.