Not a great deal of explicit category theory in this. Somone ought to implement Moggi's paper on exceptions and show exactly what the constructions mean.
Yes. Many category theorists would find Moggi91 opaque. It could benefit from commentary and more detail than would be standard for a published paper, if the intention is to make the categorical semantics of functional programming with side effects accessible to a wide audience. I guess one could suss this out of Robert Harper's book on the foundations of programming languages, but I was thinking of something more direct.
http://www.cs.cmu.edu/afs/cs/user/crary/www/819-f09/Moggi91....