So once again the world is in the Pangaea formation and the plates are moving on the same trajectory to form the continents that the world is in today (I'll refer to it as Modern). Instead of moving at the rate of 2 inches a year (as it is now) it is moving at a rate that would put the continents in the Modern Formation in about 2000 years. What sort of effects would there be? I think there would be earthquakes, since the ground is shifting, but would there be other disasters and things that impact the environment and people?
The tectonic plates will be moving six orders of magnitude faster.
It's hard to figure the numbers for that, but you can expect that the crust will crack and melt.
Quakes release a huge amount of energy. You are talking about making them somewhere between one million times more intense. The Richter scale wouldn't be enough to measure it.
I don't think your continents (if you get any) will look like the ones we have today. Don't forget, they were not made by tectonism alone. A lot of erosion, ice ages, meteor impacts etc. took place too.
More likely, your Earth will go through a second Hadean period.