I know this isn't a solve critique thread, but I couldn't help myself.
Bottom line is:
NEVER ROTATE TWICE FOR AN F2L PAIR, DON'T BE AFRAID OF LU-GEN SOLUTIONS
5. (11.68) R2 F2 L D B2 L2 F' L2 D2 L2 U F2 D' B2 D' F2 D2 L2 U' L D
y2 // inspection
L' U R U R' U' R' U' R' U R' // cross
x2 y' U R' U' R y U' R U R' // 1st pair
y2 U R' U' R y U' R U R' // 2nd pair
y' R U' R' U R U' R' // 3rd pair
y' R U R' U2 R U' R' U R U R' // 4th pair
U' R' U' F U R U' R' F' R // OLL
U2 R' U2 R U2 R' F R U R' U' R' F' R2// PLL
U // AUF
Cross: LUR-gen algs are not that fast (though not the worst), and because of the L' and the blue cross piece that will go up, pieces are going to move anyway.
So there's really no excuse for not doing cross on bottom, especially when the cross is that easy.
z2 y U' R2' F U' B2'
F2L 1: No need to rotate and rotate back, just do U2' (R' F R F') U2' R U R'.
Even if you did y' U R' U' R, at least rotate again so that you solve the pair in the back.
F2L 2: You can solve this pair in the front with U' M' U' r' F R L' U L, but a better solution would be to solve it in the back with U2 L' U' L U y L U' L'
Please never solve a pair with a y2 and a y ...
F2L 3: OK
F2L 4: No need to be afraid to use L moves, you can solve this case with either (L' U' L U) L' U2 L U L' U' L or (L' U L U) L' U' L U2' L' U L
5. (13.76) B2 F2 L2 D R2 B2 U' B2 R2 L' D F' D L2 D2 F R' F'
x
R D' L D' R' // cross
y U R U R' y U' R' U' R // 1st pair
y' U2 R' U' R y U' L' U L // 2nd pair
U R U2 R' U R U' R' // 3rd pair
y2 U' R U2 R' U' R U R' // 4th pair
F R U R' U' F' // wrong alg again
// but ....
L' U2 L' U2 F2 L' F2 R U2 R' U2 L2 U2 // ZBLL !!!
Cross: OK
F2L 1: you can solve this rotationless with f R f' L' U2 L
If you want to solve it with rotations to fill a back slot, you can save two moves by doing y R U R' y R' U2' R
F2L 2: no need to rotate and rotate back, you can pair it from this angle with U' L' U' L U2' L' U L
F2L 3: OK
F2L 4: Why do a y2 rotation when you can directly solve this case in the back: U' L U2 L' U' L U L'