After taking some propane tanks from work, Hank comes home and starts telling Peggy to throw out her old computer. The clock in the background starts off at 10 o'clock. Hank then sees Dale knocking at the door and the time has changed to 1:50. After Dale comes in, it changes again to about 11:35.
Before Peggy reads Luanne and Bobby her musing about "Noel", Bobby is to her right and the shot shows them all from behind. The next shot he is to the left of Peggy and right next to Luanne, despite Luanne having Peggy and Bobby between her at the start of the scene.
Just before Hank uses the varnish on the grandfather clock you can see a quick shot of the power drill. This would have been impossible as we saw, and he told Bobby, he got rid of all his power tools the day before for some corn. Later in the scene when he wakes up the power tool has disappeared for good.
As Peggy goes for her present and rips the wrapping paper to see it's a grandfather clock, it is set at 12:35. The following shot it's at 11:55. A little later on when Hank is about to varnish the clock, the time changes again before and after he closes the garage door where he is doing the varnishing.
In the episode we see the door to the boiler room (where Peggy's computer is) the door opens outwards into the hallway. Later in the episode she comes in to the room to check on some of her printings she was doing overnight. In this scene she opens it inwards. This wouldn't be possible as the door has a knob meaning it wouldn't be a two-way door.
At the end shot you can see Kahn by his fence talking to the gang, but when he is done, it shows him just lower down until the fence is gone. It is not a natural movement at all.
The gift of toilet paper that Luanne gets actually is labelled "To: Bobby".
Tagline: "You will be begging for gerbster!" -Dale
Surely a man experienced at DIY building and repairs knows that you do not varnish, use aerosol spray paints, etc. in an enclosed space. Yet, Hank does just that with the garage door down.
Peggy says she's going to take the kids out to get presents, yet it is Christmas Day. Most stores are closed.
(Hank burns the rolls of toilet paper)
Kahn: Hey, hillbillies, those aren't logs, you know. Yeah, they for wipie-wipie.
(At the dog shelter)
Chappy: Please, my wife is in a wheelchair. All she wants for Christmas is a big fat dog with lots of meat on his haunches.
Dale: I'll take all nine of those little dogs on top. Wrap them up.
Dale: Hank, I have dedicated my life to getting ahead of others in times of crisis. This is my time.
Hank: Fine. It's your time. So what do we do?
Dale: I have no idea.
Peggy is at the Megalow-Mart and she runs into a Dell employee and asked about her Kaypro's Y2K compatibility.
Dell Employee:Kaypro! My watch has more memory than that piece of crap.
Chappy: I live in a shack, and I poop in an outhouse.
Hank: There's not a Mrs. Chappy, is there?
When Hank is varnishing the grandfather clock in the garage, he says to the picture of Tom Landry there, "I bet you're ready for the millennium, Coach Landry!" Tom Landry was only just barely ready for it; he died in February 2000.
The "Dew, Mountain" is probably a take-off of the Army method of naming supplies. For example, in MREs they have "chicken breast, grilled and char-marked" instead of saying "grilled chicken breast."
The Arcade store name that appear JRR Tokens is a parody of J.R.R. Tolkien the "Lord of the Ring" author
The episode title The Hillenium is a take-off on the Millenium.