I am attempting to create a long shadow on my icon by using this effect in Illustrator. When I use Object > Blend > Make it leaves white spaces between each shape it creates and looks extremely ugly. How can I fix this?
Change your primary blend objects to have a fill and no stroke rather than just a stroke.
When you blend objects with just a stroke, you need to increase the number of blend steps so that the gaps between strokes doesn't appear. By simply using a filled shape for the blend you can achieve easier blends.
Note in your tutorial link filled shapes are used, not merely stroked shapes.