SQL Server Join Warning – Should I Be Alarmed by NO JOIN PREDICATE Warning?

Not sure what you mean, but I think you are looking for something like this:

Case 
  when A_staff_Service_Type.type = 'v' and pt_service.service_code = 'N06' 
     then isnull(Indirect_Duration,0)/60.00  + isnull(direct_Duration,0)/60.00 
  else null 
end

I also don't know if the AND is correct for your use-case. Maybe you want an OR - but based on the little information you have provided this is impossible to answer.

The obvious answer to "I want the results added" is:

Case when A_staff_Service_Type.type = 'v' 
  then isnull(Indirect_Duration,0)/60.00 else 0 end 
+
Case when pt_service.service_code = 'N06 ' 
  then isnull(direct_Duration,0)/60.00 else 0 End

What is up with FROM part JOIN model ON 1=1? This the same as FROM part, model, which is a cartesian join and will result in a very large number of rows. Is that join supposed to be like that?

You will likely help us help you if you provide details about the tables involved. Please "script" the definition of the tables, along with any indexes defined on those tables.

This sounds like a classic case of parameter sniffing resulting in good plan/bad plan choices for various scenarios in your data.

You may be able to get more reliable performance by making SQL Server cache different plans for different scenarios by using sp_executesql, as in the following example:

CREATE PROCEDURE [dbo].[create_grid_materials2] 
(
    @partlistid bigint
    , @pid bigint
    , @masterid bigint
)
AS
BEGIN
    begin
        DECLARE @cmd NVARCHAR(MAX);

        SET @cmd = '   
        INSERT INTO material (partid, personid, modelID)
        SELECT 
            partid = part.id
            , personid = @pid
            , modelid = model.id  
        FROM part
            INNER JOIN model ON 1=1
        WHERE (
            model.masterid = ' + CONVERT(NVARCHAR(50), @masterid) + ' 
                AND model.modelSetID IS NULL
                AND part.partlistid = ' + CONVERT(NVARCHAR(50), @partlistid) + '
                AND (
                    part.partType = 100 
                    or part.partType=120 
                    or part.partType = 130
                )
            )
            AND NOT EXISTS (
                SELECT 1 
                FROM material AS a1 
                WHERE a1.partid = part.id 
                    AND a1.personid=@pid 
                    AND a1.modelid=model.id
                )';
        DECLARE @Params VARCHAR(200);
        SET @Params = '@pid INT';
        EXEC sys.sp_executesql @cmd
            , @Params
            , @pid = @pid;
    end
End

The above code will cause a new plan to be generated for each combination of @partlistid, and @masterid.

The presumption here is some combinations of those two variables lead to a very small number of rows, whereas some combinations lead to a very large number of rows.

Forcing a plan for each combination allows SQL Server to generate more efficient plans for each. I've explicitly not included @pid since you probably want to try it with a fairly small number of combinations first; adding a third variable to the mix will make for an exponentially larger number of possible plans.