Whenever I create a square shape at 100% zoom, I get perfectly sharp edges. However, once I zoom in at any amount, drawing a perfect square (without anti-aliasing) is very difficult. Is there a way I can turn this off?
Firstly you set the shape mode to "fill pixels", you can't turn AA off with shape layers:
Secondly you need to uncheck the "Anti-alias" checkbox (this only appears after you do the first step)
Here I am zoomed in to 800%. The rectangle on the right was drawn with AA on, the rectangle on the left was drawn with AA off.
If you need to retain the shapes and don't have to be pixel-perfect about the anti-aliasing, you can use selections as a quick & easy guide. Selections always snap to-pixel so they are better "pixel guides" than regular Guides.
Zoom to 800% (or some other high zoom)
Draw some guides and make a selection.
Using the Rectangle shape tool, draw a rectangle that matches the guides and another rectangle that matches the selection.
You'll notice that the guide following the selection is not perfectly aliased, but it's pretty close and probably not be noticeable at normal zoom (keep in mind that if you're zooming in for sub-pixel edits, you're taking a much closer look than most people will).