This episode broadcast exactly 17 years after 'Simpsons Roasting on an Open Fire', the first episode of The Simpsons.
This episode takes place over the course of an entire year, from December 24, 2005-December 24, 2006. This is clear because of the listed dates of holidays that take place on certain days of the week listed on the calendar. In 2006, Martin Luther King Day does take place on Monday, January 16, while Columbus Day is on Monday, October 9 and the day after Thanksgiving is on Friday, November 24. This means that the episode began to take place 1 year in the past (during Season 17, which the episode Simpson Christmas Stories would have taken place) and works its way up to the present 1 year later.
It's possible that for the past year in the series (after Martin Luther King Day actually), Gil could have been living in the Simpsons basement this whole time, since it wasn't seen in any of those episodes. The only one of those episodes in which he appeared at all was Jazzy and the Pussycats. This is not contradictory to which that episode takes place, since it aired before November 24 (when Gil moved away back to Scottsdale), and he could have gotten outside the house for a while.
Gil's surname is revealed to be Gunderson. This may be a reference to a character from Fargo with that surname, whose first name is Marge.
Despite the title, Marge (or anyone) does not actually try to kill Gil.
This episode has a different opening sequence. Instead of the normal, regular opening sequence, the town of Springfield has snow and everything is Christmas-themed in the opening sequence. Other episodes to have Christmas-themed openings are Season 20's The Burns and the Beesand Season 25's White Christmas Blues.