Lots.
If we're talking about the early 80s, then yeah, South Africa could go nuts, massively upping the ante in its support for the insurgencies fighting the governments of Mozambique, Angola, and the other states that were hostile to the apartheid regime. Since most of these governments were aligned with the Soviets, the Americans might simply cheer the South Africans on, apartheid or no apartheid.
If the Soviets move into the Middle East, the Israelis are going to go apeshit, and we would quite likely be seeing the IAF tangling with the Soviet Air Force in short order. This, in turn, could bring Iraq and Syria into play against Israel, with the Soviets backing them up. No telling what Egypt might do in such a situaton.
Central America will go up in flames, for obvious reasons.
Not sure about India and Pakistan. India was generally pro-Soviet, but not overly so, while Pakistan was a strong U.S. ally. But their emnity with one another has little to do with the Cold War, and they might see no reason to get involved. Then again, the generally unstable geopolitical situation will loosen things up all over the world. No telling what might happen.
If it's before May of 1982, I wouldn't be surprised if Argentina takes the Falklands while the Royal Navy is otherwise engaged.