If you are talking about the vertices of a path then press the G key to bring up the pen tool. It's all about where you click on a path. Observe the change in the pen tool as you move around.
Thanks for replying, Rick but its not happening for me. Like I've mentioned I can adjust the vertices of the paths—it is when I keyframe the paths, the second keyframe primarily, is when the ability to adjust/move/tweak vertices goes away. I've gone through every pen tool/modifier key combination while directly above the vertices and nothing happens.
As I said before, and if you look closely I have keyframes on the paths, you have to carefully roll over the right parts of your path and make sure that the path is selected and not the shape. It takes a bit of getting used to. You are probably selecting the entire path. If you press the U key twice to reveal the path and the keyframes, select the path, press the G key to select the pen tool, then roll the pen tool over the path you'll see a pen with a plus appear. move off the path and hold down the Ctrl/Cmnd key and you'll see a white arrow. Click and drag around a vertex and now you have selected a single vertex complete with the handles.
You can also do this with the selection tool (V) but the procedure is not exactly the same and I think a little more difficult. If the entire path is selected then you cannot select an individual point, but if you hold down the Cmnd/Ctrl key and move off the path you'll see the cursor change to a white arrow. Click off the path, then you can click on a vertex and get your controls back. I much prefer using the pen tool because it allows me to draw around multiple points and transform them quickly, gives me more options though the modifier keys of Alt/Option or Ctrl/Cmnd to change the tools and generally work much faster, but you can use either one.
I think I need to elaborate more on the causality of the problem.
I have the following expression for the path which links to a control slider:
ctrl = thisComp.layer("Bad Slider").effect("Slider Control")("Slider")
small = key(1).time;
big = key(2).time;
amt = ctrl
t = linear(amt,0,100,small,big);
When the expression is applied, I lose the ability to adjust the vertices after inputing the second keyframe on the path. When I remove the expression I can adjust vertices per usual with as many keyframes as I want.
So I guess the question becomes why can't I adjust vertices of a path when an expression is applied and/or is this just how it is?
Sorry, I missed the rather obscure reference to an expression in you first post. Had I been paying more attention I would have said disable the expression to edit the path, then enable. Not being able to select a vertex with the expression enabled makes perfect sense because with it is turned on the entire path is selected by the expression all the time. That is the way expressions work. This seems like a lot of trouble to go to just to change the timing of a couple of keyframes.
I didn't fully realize the causality of the problem until your prior response, therefore I missed explaining the key component.