In the scene where Carrie is sitting in front of the mirror after she got home from school, she
gets mad and the mirror shakes then finally shatters. In the next shot back to Carrie, the mirror is cracked, but not shattered. Did her powers have something to do with this?
True.
This is a typical error because directors mostly like to shoot the special effects after the 'normal' scenes. Even very good F/X-Artists can't foresee what the effect will be exactly like.
She put it back like that with her powers, she couldn't seal the glass as it was before it was broken but could move all the pieces back to form the mirror - albeit with cracks.
She was worried that her Mother would beat her or lock her up or something if she found the mirror broken. You can see Carrie glancing at the mirror hoping her mum won't see it.
Otherwise her mum would have said "oy! you broke rhe ruddy mirror!" or something......