I am just starting to plan another DONE to requalify for AA EXP. The last time I did a RTW, paper tickets were common so there was no problem with 20 segments. CX computer prepared the ticket in Japan and I had no subsequent routing changes, so there were no difficulties. I plan to have CX issue the ticket in Japan again.

Currently are there any problems with 20 segments?

A search did not yield a clear answer to visiting CPT or JNB on a 5 continent RTW. The general trip I am thinking about is: (Stops are in bold)
nrt-hkg-jfk-sju-lax (part 1)
lax-dfw-anc-dfw-lax (part 2)
lax-lhr-dxb-lhr (this is where I would like to go to CPT or JNB)
lhr-syd-drw-per-hkg-sin-nrt

or put another way
nrt-hkg-jfk-sju-lax-dfw-anc-dfw-lax-lhr-dxb-lhr (how to go to CPTor JNB and then) syd-drw-per-hkg-sin-nrt
The validator does not allow LHR-CPT-LHR

Thanks for any suggestions.

I've checked nrt-hkg-jfk-sju-lax-dfw-anc-dfw-lax-lhr-dxb-lhr-cpt-jnb-syd-drw-per-hkg-sin-nrt against Mileage Monkey and it's happy. You just won't be allowed more than 2 stopovers in Asia, as that's your continent of origin.

Any comments from the experts out there?

(BA's franchise Comair flies CPT-JNB & QF do JNB-SYD.)

Checking with the KVS Availability Tool & looking at random dates, I see precious little D bucket availability on this flight. (Earliest I came across was mid-week at the end of June, but I'm just poking about at a few dates.) OTOH, there seemed to plenty of (limited) A bucket availability.

It looks as if you need to reserve a long way out or think about paying for a bit of pampering if you want to pass by CPT on this trip. (PS: It's worth it, IMHO.)

Not currently, but probably there will be soon.

Right, you can't return to Europe from South Africa, so you need to take the QF flight to SYD or keep it as a DONE4 and go JNB-HKG.

Alternatively, you can pay your own way from southern Africa to one of the three cities (NBO, DAR, EBB) served as dead-ends by BA, from which a transit-only pass back through LHR is allowed. Thus, for example, LAX-LHR-DXB-LHR-CPT-JNB//DAR-xLHR-SYD... would be allowed.

QF64 is tough sometimes, especially during the southern summer. Last year when we used it (August) for some reason QF held all the D seats for Mondays only - D9 on Mondays, D0 the rest of the week. They're not like the rest of us Earthlings, those yield management entities.

Indeed it would, but it would force a change in the rest of the itinerary, to stay within the 20 segment limit. (I realise it was only an example)

Since the OP wants to go to CPT or JNB it shouldn't be much of a problem.
nrt-hkg-jfk-sju-lax-dfw-anc-dfw-lax-lhr-dxb-lhr-jnb//dar-lhr-syd-drw-per-hkg-sin-nrt

Where dar could be nairobi or entebbe or farther away lagos, abuja, or accra.

Or just buy a seperate DXB-JNB/CPT-DXB ticket. Saves one continent for the RTW and makes everything much easier.

Thanks for the info and suggestions. I think I will just buy a separate ticket to South Africa and do a 4 continent.

Remember a J award ticket between Europe and Africa is just 75K AA miles. Also note that LHR departures in J result in big UK passenger duty fees.

Northern Africa still counts as Europe and you might be able to make your way from there. Might be cheaper, but not very convenient.

The cheapest tickets to JNB tend to be from IST (on TK) or DXB (on EK). I suppose CAI is also an option if you are willing to fly Egyptair. But there is a severe shortage of capacity into JNB or CPT, making for high prices during peak season. In general DXB-JNB is the best choice.

In a quick look-around for various months on ITA, I can only see a couple of origin/destination points and carriers (e.g. DXB-JNB, CAI-JNB on KQ or SA, nowhere to CPT) where the coach fare is less than the (NRT) DONE4/DONE5 differential, and nothing comes even close in business class. Not saying cheaper fares aren't possible, just not that I could see in a cursory scan. If the OP's intent is to requalify for EXP, then the points harvest might be worth the slight differential.

SA has a one-way DAR-JNB internet fare of US$280. On part 3 of his proposed itinerary, he could go LHR-DAR, buy the separate ticket DAR-JNB, then pick up the DONE* again at JNB with JNB-LHR.

Don't even think about it. As someone with far too much experience on African airlines (e.g. Air Mauritania, Toumai Air Chad, Air Zimbabwe, & a host of Sudanese 'airlines' to Darfur, known collectively as Inch'Allah Airways), the concept of trying to make my way from North Africa to the Cape fills me with considerable dread. Purchasing a pogo stick & bouncing my way would be less painful.

Just wondering if there is any particular reason for getting CX to ticket instead of AA (which I assume is your "home" airline and depository for FF miles)?
Happy Travels.