I've noticed the following:

If I am creating a paid invoice for a client and add product A to the invoice, then add a custom product B and save the invoice to generate the email notification, the email which is generated only says "This is to let you know that [CLIENT] has purchased [product A]."  Yet the invoice total will be the combined purchase price of product A and custom product B.

This should really be changed to a list which itemises each product purchased, which would obviously make the total invoice price make much more sense.

Ok, I notice that the email which is sent to the actual client lists each item.  But why is it different for the notification given to the admin?

That sounds like it could be a bug - I'd recommend submitting a ticket with steps to reproduce the issue.