I believe the answer is
An incorrect answer.
I am never correct, except for in the present, in the now, in the current.
An incorrect answer is never correct except right now? But then that means that my answer is right...omg I love this riddle.
I am hated by students, loved by teachers, purposely created, and accidentally created.
Students don't like getting the wrong answer. I suppose teachers like it when students get the wrong answer? A nice teacher might like it because it gives a good lesson to the student. An evil teacher might like it because it drags down your grade...
I deserve a cross most of the time, but in special occasions the letter before 'w.'
When you get an answer wrong you get a cross? But sometimes you get a 'v'? Like a check mark?
I am the arch-enemy of the double zeros. What am I?
The double-zeros could mean 100 or full-marks. And an incorrect answer would definitely be the arch-enemy of a 100% on a test.