CLRS Exercise 24.3-4 - Confirm Output of a Program Claiming to Implement Dijkstra's Algorithm
So I'm going to go out on a limb with this one and attempt to answer my own question. It seems that when running the algorithm given in the solution, say that there are many vertices for which $v.\pi$ and $v.d$ is incorrect (call this set of vertices, $V_i$ and $V_i \subseteq V$). 

When we run the algorithm, if there are at least some vertices for which $v.\pi$ and $v.d$ is correct (call this set of vertices $V_c$ and $V_c \subseteq V$), the algorithm is guaranteed to detect at some point that there is an incorrect vertex $u$, such that $u \in V_i$. 

But, it may return a false positive for some vertex, $u$ (again such that $u \in V_i$) if all of the parents of $u$, WLOG say a parent($u$), is called $p$, so $p$ also has incorrect distance and predecessor values, thus $p.\pi$ and $p.d$ is incorrect for a parent, $p$ of $u$ therefore $p \in V_i$ but eventually we will come across some vertex $u \in V_i$ such that when we look at the incoming edges to $u$, we will find that $u.\pi$ is incorrect, since at least $1$ of the parents of $u$, call it $p' \in V_c$ has correct distance and predecessor values, and we would return false/something that indicates we have found the vertex $u$ such that $u.\pi$ and $u.d$ are incorrect. 

In the case of all $v \in V$ outputted by the Professor's program are incorrect, we'd easily find a $v$ such that $s \xrightarrow{} v$ and see that $v.\pi$ or $v.d$ is incorrect. 

I believe this explains how the algorithm works... Someone please correct me where/if I'm wrong. Thanks.