Your trip is not valid as stated because of the 3 long-haul European sectors.
If you remove the surface/seperate ticket sectors your actual RTW itinerary would look like this:
CAI-LHR-DXB,lhr-sfo-hkg-sin-syd-jnb,cpt-lhr-cai
Running this through the great RTW validator at
http://jph.bytestacker.com/award.htm
fails because of the final LHR-CAI leg.
If you route via BCN as Unterwegs suggests then the result is valid
1: CAI-LHR: 1st of 4 (Europe)
2: LHR-DXB: 2nd of 4 (Europe)
3: LHR-SFO: intercontinental
4: SFO-HKG: intercontinental
5: HKG-SIN: 1st of 4 (Asia)
6: SIN-SYD: intercontinental
7: SYD-JNB: intercontinental
8: CPT-LHR: intercontinental
9: LHR-BCN: 3rd of 4 (Europe)
10: BCN-CAI: 4th of 4 (Europe)
Congratulations!! Valid itinerary!!! - (38807 miles)
And in fact you could add sectors in North America, Asia, South West Pacific or Africa up to a limit of 4 per region and a limit of 20 sectors in total.