If you are just learning to play... you should focus more on chords rather than playing individual notes.
The chords are the foundation of all the songs. Once you are familiar with the chords, you will see the more difficult guitar parts are a for the most part a subset of the chords and things make a lot more sense.
Johnny's lead parts on most songs are rather hard to play.
You should check out
www.guitarnoise.com for some pretty good free lessons.
You should consider lessons in person with someone who can show you why you are struggling with fingering, give you good tips on how to change from one chord to the next, help you with strumming patterns and numerous other things that you simply will take forever to figure out without a teacher.
My personal advice is don't be afraid to learn barre chords (chords where you have to lay your index finger across 5 or 6 strings).
You will never really play any Moz or Smiths stuff if you don't learn these. Learning them is easy. Making them sound good and changing to them is hard, especially at first. I shied away from them for a long time and when I was finally forced to learn them I was amazed at how much more stuff I could play. It did take hours and hours and hours of practice to actually learn to play them but it was something I wished I did sooner.
The other great thing about them is that 90% of all barre chords are so similar in formation that once you have the basics down you can play almost every major and minor chord.
Alain and Jesse are both very heavy into barre chords. When you play barre chords you don't really have to have good fingering techniques because even if you hit strings you shouldn't have, you are hitting strings that sound fine with the strings you meant to hit.
Jesse in my opinion has better fingering skills than Alain but neither of them can play like Johnny Marr let alone write like him although I hear nothing on the MM CD that sounds interesting at all from Johnny.
Boz for the most part plays what I call cowboy chords. They are all the basic chords you can play without playing barre chords. He does some other stuff but 90% of his live playing is just strumming some chords.
Oh one more thing, buy a capo. Very few moz/smiths songs are in standard tuning.
