What's an improper blood test? So long as can draw blood, it's a valid blood test. Not all veins are same size and sometimes it can be blocked/can't keep poking same vein, so the nurse will need to use other veins
Did the nurse not draw enough blood for the test? This is odd, even if anyhow poke blood is still blood, the test should still be valid. Did they ask you to go back to redo and did they say why?