Are they really LEDs? I guess it’s possible they’re pairs of LEDs, antiparallel, but why would they do that? Anyway, I can’t see how the “diodeness” could matter. You could always stick diodes in series, I guess, if you’re worried about that.
You do have all the “green” wires on the layout diagram connected to Arduino ground, right? Including the one for the LEDs?
When you say “it’s unstable” what do you mean? What behavior do you see?
Assuming you’re following Sam’s version, buttons 7 and 8 are shown as connecting to pins A6 and A7, but in his code it says:
#define STEPBUTTON7 21
#define STEPBUTTON8 20
where 21 and 20 I think are the values corresponding to A7 and A6 respectively, so seemingly inconsistent. If you change 21 to 20 and vice versa in those two lines it should fix that problem.
When you say “it seems to stick at step 5” do you mean the forward switch doesn’t always work when step 5 is lit up? Does the same happen with the backward switch? Have you tried using a clock signal in the forward/backward jacks, does the same happen if you do?