I am currently working on a world and slapped a small continent onto my antarctic region which then got me to thinking about the effects of that. The Antarctic current on Earth now gets to make a more less straight run without being directed north much to pick up warmer waters, hence making antarctica more "isolated" in its own climate. At one point Australia and South America would have altered that flow (being connected to Antarctica way back when) and sent the cold water north to warm up before it would come back down, and those warmer waters would have effects on the climate down there. In my case, it will also affect the climate of another southerly continent, making it a little more pleasant than it would otherwise have been.

Climate is so much fun it will drive you crazy.

Rivers are really fairly simple, its just easy to slip one in because you want it there rather than it logically being there, LOL.