What will happen to the Earth's surface if the tectonic plates moved faster than usual?

If the tectonic plates had higher rates of movement than what they currently do, then the surface of Earth would have been much different. The first noticeable difference would have that the average elevation would be higher than it is now. The reason for that will be that the erosion rates will remain as they are, while the orogenic processes will speed up, so there will be much faster formation of hills and mountains.

The climate would vary much faster on global level, as faster movement of the continents will contribute to fast changes in the ocean currents, and the global wind patterns, all that can have been impact on the relief.

Another thing would be the merging and breaking up of the continental masses, so a formation of a super-continent will occur, and with it lot of new land forms around the areas that are boundaries of the plates, but also that super-continent will break up quicker, so new continental masses will form quickly as well.

With the directions of movement of the tectonic plates as they are, if the rates of movement speed up, Australia will very soon merge with the southern islands of Southeast Asia, Africa (Nubian plate), North America, and Eurasia will merge, while the Somali plate of Africa will move into the Indian Ocean and close it up. South America will isolate itself from North America and move deeper into what is now the Pacific, while Antarctica will move gradually toward the Equator, all of which will make the world look much different, and with constant rise of new land forms and changes of the surface of out planet.