This is a question for you guys and gals who are pretty competent at playing faster solos.

I've been getting much better at learning and playing some intermediate-advanced solos over the past year (old Metallica, Pantera, Van Halen etc). It seems like I can play along to the songs themselves almost perfectly, but when I play the solo by itself, without a backing track, quite frankly it can sound like shit (in my opinion) most of the time. The right notes are all there. That's not the problem. The problem is that I have a bad habit of accidentally hitting or rubbing against a lot of open strings, especially when I'm releasing a bend from the string above or tremolo picking across two different strings.

I realize that the smart thing to do is to learn how to play the fast parts slowly and perfectly, without any unwanted noise, then slowly build up to playing it the same way at full speed. I believe the problem is that I've been practicing the wrong way for so long that it has become a habit that is hard to unlearn.

My question to you folks is do you have any smart tips for playing fast without hitting a few obvious unwanted notes? Maybe a palm muting technique with the picking hand that I didn't think of or a way to incorporate playing more effectively into my practice routine without relearning everything from scratch and completely reinventing my technique? Any guidance here would appreciated greatly. Keep Rocking.
It really is all to do with string muting. I make a "tunnel" with my picking hand, by making a very loose fist. The little finger side of the fist (primarily the little finger edge) mutes all treble strings beyond the string that's being played. The thumb-side of the fist mutes all the bass string side. The only string sounding is in the tunnel in between.

I also back this up with muting using the fretting hand fingers.

It's really an important skill to develop ... makes a huge difference. So I'd persevere ... and this will definitely involve looking at both hands, i minute detail (use a mirror if need be), at slow speeds, and notice which finger(s) are creating the problem, and adjust the muting to catch that problem.
You need to research "dampening "- check out the Eric Johnson tutorial video - there's one segment where he really talks about it. Next-level guitar playing is all about dampening - whether your playing slow or fast, you need to excel at it in order to have good tone.

It's a combination of the right hand and left hand.

As Jerry mentions above, it's a very important skill to develop and probably one of the most overlooked aspects in guitar.
Muting or dampening is something that comes with a lot of practice. Unwanted strings or notes is a common problem when learning, it just takes time and practice to get it right.

Also I found that practicing with a clean sound helps a lot, if you can play it right clean, it should sound good after you punch up the distortion. I practice on acoustic a lot, even some leads.

Practicing in a completely darkened room is something I also advise. Nothing develops your muscle memory and therefore accuracy like practicing when you can't see a thing.
Hmmm...I wonder what this button does...
+1 for muting and dampening. It helps with the human factor. Even Joe Satriani has to practice 8 hours a day.