Thank you for the quick reply!  I have solved the issue after many hours. 
 I hope this will help someone else.  And perhaps these steps will suggest 
a change for the next build.

First, I found a remark in an earlier thread (thank you petrs) that 
suggested using full path names for the latex and dvipng commands in 
~/Library/Mnemosyne/config.py.

Doing this fixed the shell error "command not found", but then I got a new 
error:

8/21/16 6:48:40.877 PM Mnemosyne[98179]: tmp.dvi: No such file or directory

So I made a guess that I needed to also explicitly give the path to 
tmp.dvi. Since I initially did not know the path, I tried to pass a 
parameter to latex and dvipng that would specify my own temp directory. 
 That did not work so I fiddled around with latex.py in the package and 
found that the path is:  ~/Library/Mnemosyne/default.db_media/_latex/tmp.dvi

This got me closer! Alas a new (but final) error emerged:  

8/21/16 7:04:57.836 PM Mnemosyne[98753]: /opt/local/bin/dvipng: Fatal 
error, PRE does not occur first - are you sure this is a DVI file?

After some additional head banging, I went to the /bin for my installation 
(MacTeX) and asked ls -L which showed that latex is soft linked to pdftex, 
which defaults to pdf output.  So I specified the output type and now I 
have Mnemosyne working without errors!

Before:
# Latex command.
latex = "latex -interaction=nonstopmode"

# Latex dvipng command.
dvipng = "dvipng -D 200 -T tight tmp.dvi"

After:

# Latex command.

latex = "/Library/TeX/texbin/pdflatex -output-format=dvi 
-interaction=nonstopmode"


# Latex dvipng command.

dvipng = "/Library/TeX/texbin/dvipng -D 200 -T tight 
~/Library/Mnemosyne/default.db_media/_latex/tmp.dvi"


The positioning of the latex output looks a little broken but I'm pretty 
sure the issue is with my latex formatting and has nothing to do with 
Mnemosyne.

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