Sorry, didn't watch the video before I replied. Are you using the rotate tool in object mode or world mode? If you zero out the rotation of the screw does it lay straight along an axis or is it askew? The first step would be to align the object to an axis then freeze transformation on the object's rotation.
A down and dirty method to get the screw to be straight along an axis would be to:
1) create 2 locators
2) snap locator "A" to the vertex at the tip of the screw (hold the "V" key while moving the locator. Screw should have vertices visible)
3) snap locator "B" to the center vertex on the head of the screw
4) select locator "B" then shift select locator "A" and do an "aim constraint"
5) Go to your outliner and delete the constraint under locator "A"
6) parent the screw to locator "A"
7) zero out the rotation on locator "A"
8) unparent the screw and "Freeze transformations" on the screw's rotation value
9) then you can snap the pivot point to the vertex on the point of the screw
10) delete the locators
There are other ways, but this works.