What are some good exercises and tips for accuracy for single note picking I am learning the acoustic version to mr brightside no capo the chords are not a problem can change without looking and I watch my picking hand but can't hit the single strings without hitting others only at a really slow slow pace.

What are some separate exercises I can do before coming back to the song.
Scales, my boy, scales. You don't have to read music, you don't even at this point need to know the name of the notes you're picking... You're strictly using the scale shapes as a dexterity/accuracy exercise.
(It would be NICE if you learned the notes and their relationships and how chords are made and all that... But not necessary at this point)
Play scale shapes as accurately and as cleanly as possible. Use one of the many online metronomes.
Make your pick strokes as clean and clear as you can. Remember, this is not music, it's strictly an exercise.