You are missing parenthesis. But you can actually streamline this quite a bit. I think you are looking for something along these lines.
WHERE SV00300.DATE1 Between (@Start_Date) and (@End_Date)
and
(
SV00300.CUSTNMBR in (@CUSTNMBR)
or SV00300.LOCATNNM in (@LOCATNNM)
or SV00300.Contract_Number in (@Contract_Number)
)
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Understanding and Using APPLY (Part 2) - http://www.sqlservercentral.com/articles/APPLY/69954/