Test if any columns are NULL
An extension to @db2's answer with less (read:zero) hand-wrangling:

DECLARE @tb nvarchar(512) = N'dbo.[table]';

DECLARE @sql nvarchar(max) = N'SELECT * FROM ' + @tb
    + ' WHERE 1 = 0';

SELECT @sql += N' OR ' + QUOTENAME(name) + ' IS NULL'
    FROM sys.columns 
    WHERE [object_id] = OBJECT_ID(@tb);

EXEC sys.sp_executesql @sql;