Try playing the verse riff like this - you'll find it
 a lot easier.
 VERSE RIFF
 e---------------------------------------
 B---------------------------------------
 G-----0-----0-----0-----0-----0---0---0-
 D---------------------------------------
 A---4-----4-----4-----4-----4-----------
 E-0-----0-----0-----0-----0-----4---3---
 
 LEAD VERSE RIFF (along with the above one)
 e----------------------------------------------
 B---------------5------------(7)---------------
 G----6b-r-b----------6b------------------0---0-  
 D-----------------------5------------0---------
 A----------------------------------------------
 E--0---------0-----0-------0-------0---4---3---
      

 BRIDGE RIFF - 1ST GUITAR
 e----------------------------------------------------
 B----------------------------------------------------
 G----------------------------------------------------
 D------5-----5-----5-----5-----5-----5-----5-----5---
 A----5-----4-----5-----4-----5-----4-----5-----4-----
 E--3-----3-----3-----3-----3-----3-----3-----3-------
 
 I think guitar 2 goes along the above riff with a slightest
 variation
 which I like even better.
 BRIDGE RIFF - 2ND GUITAR
 e----------------------------------------------------
 B----------------------------------------------------
 G--------0---0-------0---0-------0---0-------0---0---
 D------5-----------5-----------5-----------5---------
 A----5-----4-----5-----4-----5-----4-----5-----4-----
 E--3-----------3-----------3-----------3-------------
 
 CHORUS RIFF:
      G#             Em7
 e:----------(4)-4--3--3-3-3-3-
 B:----------(4)-4--3--3-3-3-3-
 G:----------(5)-5--0--0-0-0-0-
 D:------6-6--6--6--2--2-2-2-2-
 A:----6---6--6--6--2--2-2-2-2-
 E:--4-----4--4--4--0--0-0-0-0-
 
 I'm not sure about that fill during chorus either but this
 sounds good:
 

 e------------7---7-9-10-9-7-------7---7-9-10-9-7-10b-
 B----------7---7------------7---7---7----------------
 G--------7-------------------------------------------
 D----------------------------------------------------
 A----------------------------------------------------
 E----------------------------------------------------
 repeat!
 
 The harmonics when Layne starts talking:
 e-------------------------
 B--(7)-----(7)------------
 G------(5)-----(5)---etc.- () - means harmonics
 D-------------------------
 A-------------------------
 E-------------------------
 
 The riff after the harmonics.
 e-------------------------------
 B-------------------------------
 G-------------------------------
 D-----7b-r-4-5-8----------------
 A----------------4-5-6-----5b-r-
 E--0-------------------4-5------
 
 After playing that a couple of times Jerry goes back to those
 harmonics 
 and ends this great song.