Can anyone give me some tips on alternate picking?

In order to improve your picking speed and accuracy, you have to start by going slow.  And by slow, I mean mind-numbingly, stupidly slowly.  The goal here is to teach your picking hand and fingers where the strings are, and how to skip between them without having to look.  So if you don't have a metronome, get one.  A cheap tape recorder helps too.  Set your metronome to 40 bpm, and start doing down-picks on the sixth string, one per beat--don't bother to fret any notes.  Tap your foot to the beat.  After 16 beats, move to the 5th string (still just down picks); 16 more and move to the fifth, and so on.  When you get to the sixth string, go back up.  Then, do the same with just up picks.  After that, do it with alternate picking.  As you get to the point where you don't fumble the string changes and don't make any mistakes, gradually increase the metronome's beat rate.

If you record yourself, and spend 15-20 minutes a day on this, you will be able to hear massive improvements.  The good news is, that as you get faster and more accurate, getting even faster gets easier.  Once you get to 100 bpm, go back to 60 and do eighth notes (two per beat) and keep going from there.  When you get back to 100 bpm with eighths, go back to 60 and do sixteenths.

Very soon, you will be so bored with this you will think about giving up.  When you get to that point, combine it with your scale exercises-- that is, instead of not fretting any notes, start playing  your pentatonic scales (or whatever you're working on) in the same way, at whatever bpm you've worked yourself up to.  You will find yourself improving by leaps and bounds.