If The World Was The Same Temperatures Everywhere How Would That Affect Our Weather Patterns?

It would effect the planet in many ways. First it would effect the plants species. Different plants which can serve us in different medical and other search purposes could not survive in just one temperature worldwide resulting in extinction of many species like Cactus(Important for medical purposes) cannot survive in Colder regions.
Then comes animals. Different animals require different temperatures for their survival. Penguins and Polar bears cannot survive in Sahara and Middle Eastern states and Camels cannot survive in Antarctica or Colder regions.

Yes it would, it would affect air currents as well as weather system formations.