\documentclass{article}
\showoutput
\begin{document}
one two three four $1+2+3=3+2+1$ five six
one two three four $1+2+3=3+2+1$ five
one two three four $1+2+3=3+2+1$ five
one two three four $1+2+3=3+2+1$ five
one two three four $1+2+3=3+2+1$ five
one two three four $1+2+3=3+2+1$ five
one two three $0+1+2+3+4=4+3+2+1+0=10=5\times(5-1)/2$
one two three four
five six seven eight nine ten
\end{document}
Produces

so several inline math lists, two of which are broken over a line.
The log file lists lots of things but in particular it logs the start and end of every inline math (\mathon and \mathoff) and the end of every line (\rightskip). (Actually it does not log the start of math that starts a line as that node is discarded)
So we are only interested in lines that have those commands.
You can search for those with grep or any search tool, in this case
grep '\\mathon\|\\mathoff\|\\rightskip' file.log
produces
....\mathon
....\mathoff
....\mathon
....\glue(\rightskip) 0.0
....\mathoff
....\mathon
....\mathoff
....\glue(\rightskip) 0.0
....\mathoff
....\mathon
....\mathoff
....\glue(\rightskip) 0.0
....\mathon
....\mathoff
....\mathon
....\glue(\rightskip) 0.0
....\mathoff
....\glue(\rightskip) 0.0
....\glue(\rightskip) 0.0
So it is easy to see there are exactly two \rightskip appearing before \mathoff corresponding to two broken math lists.
Note that some \mathon have been discarded at line breaks which complicates a fully automatic test, but the information is basically there. alternatively if you know that binoppenalty and relpenalty are unique you just need to spot those before \rightskip so the two lines that end in a broken math list are both marked by
....\penalty 500
....\glue(\rightskip) 0.0
Here I just used grep and highlighted the rightskip in math by eye but you could find them automatically given a few lines of perl or python or lua or whatever.
\overfullrule=5ptfor "visual signal in PDF" and you can search "Overfull \hbox ... in lines ..." in the log file. – wipet Aug 13 '15 at 06:14\overfullrulehelp? Or are you suggesting that I also prevent inline math from breaking at the same time? I wonder though if doing that might push all the math to the next line, and then I'd still miss such instances when I reverted to turning these things off. – alex.jordan Aug 13 '15 at 08:02