I think you need to be more specific with your range. =MODE(A1:A100) would work. Selecting the whole column, I assume, tries to rationalise all the blank cells to a number, hence the #NUM! error.
I was curious so I just checked as well - I have version 2003. I tried it with the whole column ref and also got a #NUM error. Quite frankly, whole column refs scare me - it seems dangerous and plain lazy to use them. I think it is worthwhile knowing what range you are dealing with.
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