OK this is weird. Today it finally bothered me that I've never read Detective Comics #27, so I went to get a copy via the Comixology app and... it wasn't on there. That struck me as odd. I know not everything is on there, but I thought that the first appearance of Batman would be a must.
To cut a dull story short, it is available on the Comixology website (for free). So I grabbed it there then had to add it to the app via the "restore purchases" bit. The web also has #28-33 (two issues per 69p purchase) whereas the app starts at #38
Comixology is due to hit 100million downloads and are giving away free comics.
First up Spider-Men #1. You need to do it via the website instructions are below. But then just go to your mobile device and go to purchases and restore and it will be available to download to your gadget.