Looks like total number of parts and sum of them differs on bricklink
Brickset says 602 elements, brickset takes its data from Lego Customer Services.

Bricklink says 603 elements, bricklink count includes a stickersheet while brickset does not. To get the bricklink total, select "Part out" on the catalog page, it will suggest to add 603 pieces to a "wanted list".

Adding the number of elements in the back of the manual I get also 602 elements.
Going through the instructions and adding all element counts I get 598, this certainly does not include any spare parts, so about 4 spare parts seems right.

Conclusion, your set is lacking elements or you miscounted.
I think easiest would be to group by element and count and see if those counts match the brickset or bricklink list or the back of the manual inventory.
Plus side will be you have everything sorted and you'll know exactly what pieces are missing.