In this tutorial, I'll be changing the purple coloured elements to red. It's a illustrator function that I use frequently.
1. Using the direct selection tool, aka the white arrow, you select the object with the colour you want.
2. From the menu, choose Select->Same->Fill Color
3. Once every object with the same fill colour is selected, you can just click on any colour swatch to change the colour for all the objects.
You can also select objects based on other properties too. Check out the other menu options under Select->Same