When Henry gets out of bed, Tully has terrible bedhead as their conversation starts. When the view cuts back to her a second later, her hair is neatly brushed.
Henry calls an ambulance and gives the address of apartment building as 334, while in an earlier scene that day, the building is clearly marked 360.
When Henry and Wanda, two career alcoholics, meet at the Kenmore, he exclaims after their scotch and waters that he has no money left. But when they go, he leaves behind his half-finished bottle of Miller High Life on the bar. Alcoholics do this all the time.
In the convenience store, Wanda purchases a six-pack of Kingsbury Malt Beverage - which is non-alcoholic beer (if you look closely at the cans, they say "contains less than 1/2 of 1% of alcohol by volume). Not in keeping with her and Henry's predilection for liquor.
When Henry and Wanda are alone in her apartment, Henry tells her that the first thing he noticed about her were her legs. When they first meet at the Kenmore, Henry first pays her attention from across the bar, she seated in a way that he could not see her legs.