I'm going on a driving holiday from Nairobi to Capetown in a 3 car convoy. What countries could cause safety problems?
All of them unless you take proper precautions. Assuming you are (and travelling in convoy is a great start) I'd say Zimbabwe would be the greatest concern and because of the political instability and borderline anarchy caused by it.
Tanzania: car jackings are pretty common, including the Tour Drive on the Masasani penninsula (the convoy will help prevent this) and it's recommended you don't drive at night anywhere in Tanzania.
Mozambique: the roads are pretty terrible, and watch out for landmines if you stray off the beaten path. You'll probably have to pay bribes to police at the numerous roadblock/checkpoints.
Malawi: in 2011 has had problems with shortages of fuel. The rural roads are, well, African.
Botswana: the rural roads can be bad, but they almost always involve long distances, loooong distances, so make sure you plan to have adequate fuel.
South Africa: Much better roads and highways (which will come as a relief), but South Africans take advantage of them and the relaxed police attitude to speeding, so high-speed crashes are quite common. almost 8 years ago