Note that for BA flights in L, you only get 25% points in the QF program, so that will include LHR-BOM. If you returned via SIN or BKK instead of BOM, you would get 100% points on either QF or BA flights according to this announcement (valid until June 2005)

Take AY on the HEL-LHR leg to ensure you don't get caught in the 25% points on BA. Take QF107 on the LAX-JFK leg to get full points.

So my calculation for a QF Silver member is as follows:

QF BNE-LAX = 7166 miles, plus 25% Silver bonus = 8958 QFF points, 40 SC
QF LAX-JFK = 2467 miles, plus 25% Silver bonus = 3084 QFF points, 25 SC
AY JFK-HEL = 4117 miles, no bonus = 4117 QFF points, 25 SC
AY HEL-LHR = 1149 miles, no bonus = 1149 QFF points, 20 SC
BA LHR-BOM = 4486 miles, BA 25%, no bonus = 1121 points, 25 SC
QF BOM-SYD = 6308 miles, plus 25% Silver bonus = 7885 QFF points, 40 SC

Total miles = 25,693
Total points = 26,314
Total SC = 175

Note that the mileage for BOM-SYD may vary slightly, depending on the numbers QF use. I have used real QF numbers for miles for BNE-LAX, LAX-JFK, HEL-LHR and I have used Great Circle mapper miles for the other flights.

I am assuming this is a Global Explorer fare, being LHGLOB26 or LLGLOB26 fare basis.

Note that when including ground sectors, the miles for that ground sector must be included in the total. I believe on a xGLOBxx fare, you can have an open-jaw at the completion (ie start in BNE and end in SYD), so long as you start and finish in the same country. But some may interpret these two rules as meaning you must include the SYD-BNE miles in the total calculation. There is no specific reference to this in the rules, so it may depend on individual interpretation. Personally I don't think it should be included, but the ticket issuing agent may thing otherwise.