Some techniques that were educational or helpful:

6.2.4:
Measure in the Hadamard basis and transmit the result.  This allows you to break [qqq] into [qq] after correcting.

7.2.3:
Notice that (Z \times I) (|00> + |11>) = |00> - |11>.
On the other hand, (X \times X) (|00> + |11>) = |11> + |00>.

8.3.2:
The equality should enter as a line of the matrix (to be inverted), but no contraint is extracted from that row of the result.  Care must be taken to make these arguments with more than three equalities or inequalities (the matrix is not square), but in this case one of the inequalities is redundant.  The conclusion ends up being simple and intuitive.

9.1.1:
Pauli operators anti-commute.

9.4.2:
The bound requested in the book is incorrect.  However, you will obtain the best possible bound by using the hint, from which you derive the bound 2\sqrt{e(2-e)} which is less than 2\sqrt{2e}.  Another method developed by a student simply uses the triangle inequality and the gentle operator lemma twice.  This obtains the bound 4\sqrt{e}.