Among the debris in Elmo's fireplace after Santa leaves are some packing peanuts.
The footage of the inside of Santa's workshop, seen in the window of the model workshop, shakes as the camera pans around and zooms in towards the model workshop.
Even though Elmo and his parents are Muppet monsters who stand between 2-4" tall, all their furniture is sized for ordinary humans.
The interior sets of Santa's workshop don't match the exterior in size or layout.
After Elmo wishes it was Christmas every day, Santa takes the only reindeer on hand (Lightning) to go visit Elmo on Sesame Street. As Elmo leaves with Lightning to see what his wish will mean for the future, Santa mentions he's going down chimneys again that night. But Elmo just left with Lightning, who was Santa's only way of getting back to the North Pole.
The fix-it shop remains closed throughout the year because of Christmas, yet many stores are clearly open, as everyone continues to buy gifts and food for their turkey dinners. There is no explanation as to why one type of business must remain closed while others are open.
After Elmo undoes his wish, Snuffy comes home to Sesame Street on Christmas day to see Big Bird. There was nothing about it being Christmas that kept him at his granny's, so he should have been able to come home during the year when it was Christmas every day.
When Lightning is flying Elmo forwards in time, to Easter, Elmo says they're coming up on Sesame Street. The globe behind them is spinning so fast, they make several more laps of the Earth before even finishing their conversation.
When Elmo goes back in time to prevent himself from ever taking the magic snow globe (thus preventing him from wishing it was Christmas every day), the Elmo and Lightning that originally existed in that timeline somehow disappear and are replaced by the Elmo and Lightning who traveled a year into the future. If all Lightning is capable of doing is flying so fast he can travel through time, there's no reason their time travel should make such drastic alterations to the fabric of reality.