All shopping cart software I know of sends the store owner an e-mail about each purchase with the customer's e-mail and payment amount. E-mail already appears on my lock screen.

It's definitely not a privacy issue but perhaps a security one. I know I wouldn't care myself using it but I would be aware that a lot of people would. I'm developing another login screen here today and part of me is wondering why we secure passwords on single user devices like the iPhones but not necessarily tablets/laptops which can often hook up to external monitors or projectors. I think the iPhone security constraints can be a little more lacking than tablets and laptops in this way because they're a little more intimate. Texts messages already show up in lock screen too and texts are considered private by most people.

The notifications are all optional: you can opt into daily summary, new payments, and new customer notifications in the app settings.