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That depends on what quicker means.
If you mean quicker for SQL Server to execute, one thing you could do is write a trigger than updates a bit column that specifies if the entire row (other than the bit and primary key) are NULL. But, there should be a REAL good reason for this as it will impact your update performance. Indexes on those columns would help as well.
If you mean quicker to write, you could have SQL generate the where clause for you. But, unless you do this alot, it isn't worth the time in my opinion.
Teaching-to-fish-instead-of-giving-you-the-fish kind of answer here:
One way of doing it is by creating a Stored Procedure that assembles and runs a dynamic query.
The Stored procedure will:
OR statements for that table's columns.