When Scrooge begins to give bags of money to Rat and Mole, there are six bags of gold in the jacket. But once he throws them all, eight bags appear. Then once Scrooge leaves, the next shot has nine bags.
When Scrooge flies out the window of his room with the Ghost of Christmas Past, he loses his slippers. Later, in his counting house, they're back on his feet.
When Jiminy Cricket (The Ghost of Christmas Past) jumps onto Scrooge's bedside table, the time on the alarm clock reads 2:00. In the shot of the curtains moving when Scrooge hears the dinging, then goes back to sleep, the time reads 1:00. Then in the next shot when The Ghost of Christmas Past dings the bell on the alarm clock again, the time reads 2:00.
In the final scene at Bob Cratchit's home, the lettering on the "Home Sweet Home" sign changes between shots (particularly the word "Sweet", which alternates between uppercase and lowercase in different typefaces).
When the Ghost of Christmas Past (Jiminy Cricket) rings Scrooge's alarm clock, the Roman numeral 4 on clock face is shown as "IIII". In the next shot, when Jiminy tries to wake up Scrooge; and later, when Scrooge is back in bed, right before the Ghost of Christmas Present (Willie the Giant) appears, the Roman numeral 4 is now written as "IV".
When Scrooge is going through his records, he pushes two equally big stacks of coins together into one. However, the new stack doesn't increase in size, when it should be twice as big.
When Jacob Marley (Goofy) tells Scrooge that he will be visited by three spirits, he holds up two fingers instead of three. This is more than likely part of Jacob Marley having the same humorous traits as Goofy.
Bob Cratchit's salary is mentioned as being two shillings and half a penny per day. In the original story, his salary was mentioned as being fifteen shillings per week. With Sundays off, that makes 2.5 shillings, or two shillings and sixpence per day. That said, "Mickey's Christmas Carol" is more an adaptation of the original story rather than a direct retelling, so there can be room for slight differences as in this case.
In the first shot inside Fezziwig's Party, the fox temporarily disappears for three frames. They possibly forgot to put his cel in there for that shot.