In 2.6 Example 1 equation \begin{equation} \psi(x) = p(-x/c) - \phi(x) \end{equation} is not correct, the correct one should be \begin{equation} \psi(x) = p(-x/c) - \phi(-x) \end{equation}. OK

Also in the end of this example, statement " this formula defines u(x,t) as 0 < x < ct solution is given by (4)" does not flow. I think you meant "this formula defines u(x,t) as 0 < x < ct, recall for x>ct solution is given by (4)". OK

Also before example 5, equation (31)' seems should have been minus sign before the first integral, not a plus. also for the first term shouldn't it be 1/2(g(ct+x) minus g(ct-x)) instead of plus?

NO, this is even continuation (for "primed") equations

For 1D wave equation on the finite interval, below the graph, section (b), ...(f.e...Ux|x=a =...) should be (f.e. Ux|x=b = ...).

Already reported and fixed

below this line ABB'B'' does not seem right, also AA'C'B'B should be AA'CB'B I think. and statement " u is defined in the intersection of..." should be " u is defined in the union of ..."

No, intersection: as $u$ is defined where both $\phi(.)$ and $\psi(.)$ are

Please verify