The simplest way is to open the Web Inspector.
This can be done from Google Chrome: View > Developer > JavaScript Console
That logs each item that is cached and shows any errors.
Safari has a similar console and can be combined with the iOS Simulator.
The nice thing about using the console is that it requires no extra work and is not something that the user typically sees.
Here's some sample output from the console:
... example.co.uk/:1 Application Cache Progress event (1657 of 1658) http:/example.co.uk/assets/images/item_35860.png example.co.uk/:1 Application Cache Progress event (1658 of 1658) example.co.uk/:1 Application Cache Cached event
Alternatively, if you want the user to see a message, you can craft some custom javascript.
Examples: