When Holmes first addresses Zeddemore by name, Peter's jumpsuit is the wrong shade of brown. It matches Ray's uniform.
Sherlock Homes explains he knew the Ghostbusters' names by reading their uniform name tags. However, only Egon's tag is visible in this scene (after Holmes gives his explanation) whereas the names are always visible in the live action versions of the characters. Further more, Spengler's tag is visible on his right breast, in the movies it is on the left.
When the Ghostbusters return to their HQ after trapping Sherlock Holmes, in one shot, the trim on Peter's jumpsuit is pink.
On Sherlock Holmes' farewell message to Winston (written on his football), the word "exciting" is misspelled as "excitng."
When Slimer is looking at Egon's calculating device, the computer graphics move out side of the boundaries of the screen.
After Holmes is released from his trap while playing his violin, Winston is heard, but Ray is seen speaking (the colors of their character models, seen from the back, have been swapped by mistake).