When I'm playing a song while looking at my finger placement I tend to hit the wrong string from time to time or I just "skim" another string lightly by accident.
I've been playing for about 8 months now and I dont know if this should still be a problem at this point.

Any tips or will this problem just fix itself over time?
"I'd rather be hated for who I am, than loved for who I am not."

~ Kurt Cobain ~
I have that problem too. I've been playing for 3 months. All I do is when that happens. I STOP IMMEDIATELY. I've read time and time again that it is key to stop and place yourself in the right position. So what you do is: Say you hit the 3rd string when you are supposed to hit the 2nd (making this simple). YOU STOP. Look at your picking hand and watch it pick the 2nd string a couple times. Then go back to looking anywhere else and try it again. If it happens again then you stop again and repeat. I find this is a good mind and hand coordinator. It's like training your mind to memorize the feeling of the right placement. You may be able to find better advice but I suggest you do this with everything. Even when your doing scales, if you press your finger on the wrong string or fret. STOP. Then watch your finger place itself on the right positioning. Then proceed.
Quote by Macabre_Turtle
Your guitar will be infinite. Far over 9000.

You could try a string skipping exercise.It doesn't matter what notes u r playing here. just play one string then skip a string and play the next, so on and so on.

so like this
--------------(1) Play here
--------------(3)play here after step 2, then down to 4
--------------(2) then here, then up one
--------------(4) play here next... and you get the point.

Once you can skip without hitting other strings... then you should be fine and able to do things like the "chugs" in Over the Mountain and Crazy Train.

Hope I helped.
Ill take that into consideration, thanks.
"I'd rather be hated for who I am, than loved for who I am not."

~ Kurt Cobain ~