Agree with the original poster.
I had my first chat from a customer today using the App - or I should say I received a notification that there had been an attempt by a customer to chat but I was doing housework and missed it.
I was surprised there was no way to see WHAT product/page they were viewing when they asked their question. Makes the shop owner seem goofy to not know something quite so basic. There should also be some sort of "away" message to let the customer know there's another way to contact when someone is not sitting there. I think most of them understand it's a small business they are dealing with. But I hate the idea that someone out there was left hanging.
Hopefully they try again but not an outstanding first impression for me. I can't tell from their question what they were even viewing.
I also wish there was a desktop page or app that can be used to chat with the customer as well. I am keeping my iPad close at hand but most of my day is spent in front of my laptop and it would just be way easier for me to type responses than peck them out on the screen. A mobile app is nice but shouldn't be the only way to use this.