Actually, you can get to JNB direct from HKG on CX, so you don't need to go to Africa via Europe. You can also get there (JNB) direct from SYD on QF (and a codeshare from PER)

I agree that the glaring route gap is to Africa, but the gap is across the S.Atlantic, which means that it is impossible to go RTW without going via Europe (unless you take the flight to Delhi, or a Royal Jordanian flight from AMM to JFK or ORD (assuming Amman is counted as being in Asia)).

Star Alliance has a similar gap but across the S.Pacific-Air New Zealand don't feel it's an economic route.

One World is actually pretty weak up and down the West Coast of the US-you end up using Alaskan on codeshares to places like SEA, PDX and OAK.

How can OneWorld's network improve?
 

By co-operation!

This strikes me again and again: oneworld is a collection of islands.
Admittedly some of the worlds finest like CX, BA, QF and even AA in their homeground (then again you have IB and Malev...).
But is there co-operation? Besides special round-the-world tarifs?
Why is SIN still the main link to Australia(instead of HKG or KUL)? Why can you not book reward flights with other oneworld carriers with BA online? Why do X and QF compete more than co-operate? Why is China excluded by preventing Hainan to enter?
Don't get me wrong: I like to fly oneworld. But in Star Alliance and even in Skyteam co-operation is teken much further.

Many routes do not have ATI, meaning that they cannot cooperate to coordinate schedules - otherwise, they'll face legal action. QF and CX is an example for the Hong Kong - Australia market, even if they wanted to cooperate, they can't because there would almost be a monopoly on several routes.

That's why I stated in one direction or the other - i.e. for a RTW you will have to pass through Europe from the Americas to get to or from Africa.

That doesn't make a difference.
With Oneworld there is currently no way to get from Africa to North or South America without touching another continent. This is what makes an xONE3 from the southern hemisphere impossible. Weather you are traveling west or east makes no difference.
Either AA or LA need to start a transatlantic service to Africa (eg SCL or JFK-JNB), QF needs to extend its EZE or JNB across the Atlantic (eg QF17/18 SYD-EZE-JNB or QF63/64 SYD-JNB-EZE), or an airline that already flies transatlantic from Africa joins Oneworld (eg, MH with KUL-CPT-EZE).

For XONE AMM counts as Europe.