I'd also recommend earthscience.SE.
Just off the top of my head, there will be geomorphological features caused by the collision that brought the continents together, and then by the rifting that broke them apart. Additionally, they gain accretions as they drift in opposite directions.
For an example of features caused by the collision, consider the Appalachian, Atlas, and Caledonian mountains. Although they're on opposite sides of the Atlantic today, they were once the same mountain chain, as high as the Himalayas. However, that was back when there were still dinosaurs, and most of that rock was eroded away in the Northern Hemisphere by ice sheets during the last ice age. In the US, it became the flat coastal plain just to the east of the Appalachians. In Norway, is was ground down to form Denmark. What we see in these mountain ranges today, on opposite sides of the ocean, is the same granite bedrock that was the roots of that ancient mountain chain. It's been uplifted again, and erosion is creating more mountains out of the granite, in both places.
The rifting process would have caused the crust under certain areas to thin and weaken. Upwelling magma would have first created a long plateau, about one mile high, along the top of the rift. Then, the stretching would have torn the supercontinent along the rift. When this happened, a deep and wide valley called a graben would formed between mile-high cliffs:
Eventually, this valley would fill with water and become a long sea, and then an ocean like the Atlantic. But you're interested in the effects of this that will still be visible. To put it simply, the sides of your continents that were affected by rifting (if they haven't been eroded like the Appalachians,) will have steep terrains on the sides facing the ocean. You can find examples of this in Africa, which was considered inaccessible for a long time due to steep terrain a mile in from the oceans; India, which has the Deccan Plateau surrounded by the Ghat ranges next to the seas; and in the Australian Alps along the Pacific coast.
You can watch a video about the Australian Alps to get an idea of what kind of terrain would result from rifting, assuming it's in a temperate climate zone, here:
Finally, as your continents move away from each other, assuming they are subducting oceanic crust along their forward edge, they will create volcanic islands out in front of themselves. These are called island arcs.
Eventually, your continents will run into these islands like snowplows. When they do, the islands will get glued to the front of your continents and start traveling along with them. The farther apart your continents are, the more material they will have accreted onto their leading edges.
You can get an idea of what the process of accreting California and the rest of the west coast onto North America was like here:
Oh, and one last thing - I just thought of fossils. If your world has fossils, and its inhabitants understand them, you might want to consider if the species was distributed across both continents when they were connected. One of the major pieces of evidence in favor of continental drift in our world was the discovery of the same animal and plant fossils in South America, Africa, India, Antarctica, and Australia.