The 'vegetable men' on the wall behind Phoebe in the restaurant are iconic portraits by a 16th century Italian painter Giuseppe Arcimboldo.
The waiter tending to Phoebe and Joey is Dan Bucatinsky who is an actor, writer, producer and director of 'Web Therapy' which stars Lisa Kudrow (Phoebe). Dan plays her assistant Jerome Sokoloff. They both also would go on to have recurring roles in Scandal (2012).
This is the third time Phoebe's birthday is shown. The first time was in The One with Two Parts: Part 2 (1995), and the second time was in a flashback in The One Where They All Turn Thirty (2001).
Chandler says that in Hawaii cigarettes are called "lei-lana-lukus". The word used in Hawaii is actually "sigika"
In a previous episode Phoebe says her birthday is February 18th. This episode is in October.