I realise this may sound daft...but practise without distortion...If you can play cleanly with a clean tone, you can control your distortion. By practicing without any distortion you're able to hear what's being played and isolate any "problems" (duff notes, ringing open strings, etc) that you might not want...
Also, practise slowly, this again helps with accuracy - it doesn't matter how fast you can play if only 1 in 4 notes is actually played properly...
Pay attention to both hands - if it's the lower string that are making a noise (E A D) then rest your picking hand (right for most people) on the bridge and dampen those strings, if it's the upper string, (G B e) then use use the underside of your fretting hand fingers to mute them.
Hope that was helpful and made at least some sense...keep at it and before you know it, you be playing note-for-note perfect solos in no time!