Ann Lassiter requests hotel phone records from 10 months earlier, in March. This indicates the story takes place in January, which coincides with the original airdate.
When a wanted US citizen goes to Mexico, the NYPD can't just go and bring them back. Mexico would be willing to hold them within the constraints of Mexican law, but there would have to be extradition proceedings before they might (or might not) be returned to the US. There is, however, the matter of her Mexican visa. Overstaying that might get her expelled.
The music at the party near the start of the show is an instrumental (piano) version of Alone Again, Naturally, a 1972 international hit by Irish pop artist Gilbert O'Sullivan. His other hit that also made it in the USA was Claire.