After Danny has been to see his son for the first time, he returns to the Hilton and is seated at the bar, apparently drunk. There is a glass in front of him which is empty except for some melted ice. Mary enters the bar and politely tries to tell him he's had too much to drink. Danny points out there is only water in his glass. Mary orders a tequila and soda and the bar tender serves her but does not refresh Danny's glass. Following this, we see the bar tender polishing the glasses and in the next shot, we see Danny's glass now contains alcohol.
Near the end, Danny Collins hands over his credit card to pay for his hotel, but never bothers to get it back. That's because he is turning in his room's key card, not his credit card.