Goofs

(at around 21 mins) When Jack's telling the people about Christmas Town, some of them keep switching places. The Clown with the Tear-Away Face is in the first line at the start, then later in the second line, then back in the first line, only on the other side; the guy with snake fingers goes to the first line to the second one, then back again; the werewolf switches place with the devil.

(at around 36 mins) During "Kidnap Mr. Sandy Claws", Shock has black gloves that disappear and reappear throughout the song.

(at around 29 mins) When Sally is raising the basket up to Jack's window, Jack is writing on the chalkboard. When he stops writing, the chalk he is holding disappears.

(at around 1h 10 mins) When Sally is picking the petals off of the dead flower on top of the spiral hill at the end, the petals disappear when she drops them.

(at around 1h 9 mins) Near the end, when Jack puts a kid on the Mayor's hat, he's doing it from the left, as both his arms are on the left of the hat. In the next shot, he's holding the kid with his arms from both sides of the hat.

At almost dead center, two red dice are thrown and come to rest, presenting "snake eyes" (both have one pip up). The one to the right shows six on the side. But standard dice cubes have opposing sides that add up to seven, so the six should be on the bottom.

If the moon is full on Halloween, then it will be waxing on Christmas Eve, not full again.

There are 59 days between full moons, and there are 55 days between Halloween and Christmas day. This is close enough that the moon could appear to be (nearly) full on both days, especially in an animated fantasy. [Note: IMDb Guidelines state that "big allowances" are made for artistic license and suspension of disbelief.]

(at around 21 mins) As the Mayor turns on the reflector light at the town meeting, some bats fly off it, scared by the sudden light. The wires that they are suspended by can be seen.

When Jack is in Christmas Town, at one point he jumps across from house to house. For about several frames, the wires suspending the puppet can be seen.

(at around 6 mins) When Jack flips a coin to the street musicians, the wire holding the coin up is visible for several frames.

(at around 14 mins) After he discovers Christmas Town, Jack accidentally stumbles down a hillside. All the lights of the town overlap his body, yet those are supposed to be far away in the background.

(at around 1h 4 mins) In the cemetery, as Jack sings and gets to the line "And I just can't wait until next Halloween", the wires supporting him can be seen shining against the background.

(at around 37 mins) In "Kidnap the Sandy Claws", just before Lock launches Barrel across the room, Lock is singing, and his words are aligned. But when Barrel begins to sing, Lock's lips are moving to the words that Barrel should be singing; Barrel's lips don't move at all.

(at around 8 mins) During Jack's Lament on top of the hill, the light being used as the moon can be seen.

(at around 1h 5 mins) When Jack returns to Halloween Town to set things right, his goal is to return Santa to Christmas Town. Yet he goes straight to Oogie Boogie's house, even though there is no way he could have known that Santa was there, because Lock, Shock, and Barrel didn't tell Jack where they would take Santa, and Jack had no reason to suspect Oogie was involved at this point.

(at around 15 mins) Jack doesn't know what snowflakes are ("What's this? There's white things in the air."), but knows what snowballs are ("The children are throwing snowballs instead of throwing heads.")

(at around 17 mins) Right before the three Mr. Hydes joins the search party for Jack to report that he just searched the pumpkin patch, his foot already can be seen in frame, ready for him to come into frame.

(at around 40 mins) Jack emphasizes to Lock, Shock, and Barrel that their mission to kidnap Santa is top secret, and no one can know. However, when they first return (mistakenly with the Easter Bunny), Behemoth is present, but Jack isn't concerned about him.

After Jack orders Lock, Shock, and Barrel to kidnap Santa, they immediately set off, and by the next scene, they are back with a wrong catch (the Easter Bunny). Jack points then them into the right direction, and the trio starts their "mission" anew. However, it takes an inexplicably long time for them to return, more than 30 days, in fact. Considering that they managed to kidnap the real Santa Claus in mere seconds and how quickly they caught the Easter Bunny earlier, it shouldn't have taken them so long.

(at around 44 mins) Santa Claus prepares the presents and his sleigh first, but only then checks which children were good and naughty. It would make more sense the other way around, unless he wanted to hand out presents randomly.