This marks the second (possibly third) marriage for Phoebe. She was previously married to Duncan the ice dancer in a sham green card marriage, and implied she once married someone in Vegas (stated in season six's The One After Vegas (1999)). In this episode, Phoebe gets married for real while this is Mike's second marriage.
When Phoebe walks down the aisle at her wedding to Mike, the song playing on steel drums is "Here, There and Everywhere" by the Beatles.
You can tell during the wedding that there is a third bridesmaid behind Monica. However, she's never mentioned.
Interestingly, Phoebe's wedding is not attended by any of her relatives, such as her twin sister Ursula, her father Frank (Bob Balaban), biological mother Phoebe Sr. (Teri Garr), brother Frank Jr. (Giovanni Ribisi), sister-in-law Alice (Debra Jo Rupp), or the nieces and nephew she gave birth to. However, there was a huge blizzard and it's possible those people weren't able to make it. In any case, it is unlikely Phoebe would have invited Ursula or Frank Senior given the intense past she has with both of them.
During the exchange of vows, Rachel is standing behind Phoebe and looking off to the side. You can clearly see she is crying. During the filming, this was the time period of the breakdown of Jennifer Aniston's actual marriage to Brad Pitt.