How many spots are identical on the average dairy cow?

That all depends on the breed. Several breeds don't have what are considered "spots." Solid-coloured breeds like Aberdeen Angus, Red Poll, Dexter, Galloway, Limousin, Gelbvieh, Canchim, Beefmaster, Brangus, Red Brangus, Jerseys, Brown Swiss and many others have no spots on them (Jerseys and Beefmasters may be an exception, as there are some purebred Jerseys and Beefmasters that can and often do have a few spots on their bodies). Herefords, Pinzgauers, Gloucesters and Finnish cattle don't really have what are called "spots," since they either have a white face or just a dorsal stripe across the back. Maine Anjous don't have a dorsal stripe, but a long line of white on the underbelly to the back legs.

Speckle Park, Shorthorn, N'dama, Ayrshires, Texas Longhorn, Florida Cracker/Pineywoods and others often have spots that number in the hundreds to thousands. Montbelaird, Simmental-Fleckvieh, Holsteins, Guernseys and others have what are more considered patches versus spots, but some beg to differ. Since I believe the question is probably specifically asking about Holsteins versus other breeds, the average number of spots on a Holstein can range from four to 10. Other breeds can be more or less. Simmental-Fleckviehs, Simmentals and Guernseys are typically less spotty than a Holstein is, and Montbelairds about the same.