I've discovered that there is one other known enzyme that finasteride directly inhibits, which is the 5-beta reductase enzyme. This enzyme produces 5-beta DHT, which has some important functions in our bodies and which doesn't seem to play any role in hair loss. Interestingly, dutasteride doesn't inhibit this enzyme.
An incubation study showed that finasteride only very weakly inhibits 5-beta reductase, with an affinity for this enzyme that is even weaker than its affinity for 5-alpha reductase type 1 (which finasteride at the standard dosage inhibits by no more than 1%). I found a thread on Tressless about this, which I've linked below. The guy who posted the thread was trying to work out if the results of the incubation study can be assumed to be an accurate determination of the amount of 5-beta reductase that finasteride would inhibit within the human body, but nobody was able to answer that specific question.
Basically, the less 5-beta reductase that finasteride inhibits, the better, as this enzyme has some important functions in our bodies and it doesn't appear to play any role in hair loss.
Here is the Tressless thread: