Failure to correct so as not to demotivate seems a recipe for disaster. If it's wrong, it's wrong.
I hope you aren't a teacher?
I agree with JT. We learn by our mistakes after all.
Psychologists tell us the best kind of reinforcement is intermittent: some (+) and some (-). This is why gambling is so addictive. Correct the galring mistakes and a few minor ones.
I think if there are a lot of minor mistakes, it would be very demotivating to see each marked out (the monstrous task of fixing them all). Instead, maybe, a few rules that they're constantly getting wrong should be written for them so they can be encouraged to check through themselves.
If worst comes to worst, cross it all out and write a big, red 'See me!'
If there are few mistakes, I think they should all be marked.