What version of Photoshop are you using????
The White Arrow tool is the direct selection tool and it work best way you point it at a path segment line and click once. When you do all the control points in a close path segment will be marked with little squares and the two control point adjacent to where you clicked will have handles you can adjust.
You can also drag out a rectangle with the direct selection tool. When you do you may select many closed paths in a path a path may have many sub paths and each has a mode like add, subtract, intersect etc, and each has a stacking order like in a layer stack. So if you drag out a rectangle many paths control points will be marked and control point adjacent to crossing rectangle will have handles. Can be very confusing.
Here are two screen capture the first on shows the layer palette and path palette. You can see many shapes and path with sub paths and modes. I also targeted layer a vector mask. The selected the direct selection tool and in the image window I pointed at the 45 degree oval path near the top right. You cab see the four control points and two with handles. The second screen capture I only captured the image window. I used the direct selection tool and draged out a rectangle and you cab see many segments control points and many have handles. I have no problem selecting what I want to select
Sorry, but you are not helping. Your screenshot shows single vector mask, which has nothing to do with the issue above.
Same problem here. Photoshop CS3. Occasionally I have a PSD file, very heavy on vector-masked layers (like 100+ overlapping layers). It happens when you are one busy UI designer. When I try to drag rectangle selection with my 'Direct Selection Tool' to select some vertices in current layers vector mask, Photoshop always fires autoselection of some completely different vector-masked layer instead. It's very annoying and there is no remedy for this but to hide all other layers or to carefully make selection vertex by vertex which is pretty painful waste of time. It would be nice to have an option to disable all layer autoselection for path tools, just like with 'Move Tool'.
"Upgrade to CC right now" is not an answer i'd like.
The screen capture shows 7 shape layers with six different vector path. The six paths have similar sub path that have different modes. I have save the six paths in the Paths palette so you can easily see them. You can see that only layer "a" and "shape 4" have the same vector path. No two shape layers are identical. You should see this in their thunbnails in the layers palette. When you target a layer you can edit its path in the Path palette it will be there (Layer Name Vector Mask) Layers can have more then one vector mask for masks can be embedded in smart objects and the layer put into layer groups the have vector mask added. All mask can be targeted and edited.