I have no idea why anyone would not use the app to read threads. (even if it was stuffed up my eyesight.
The app is not foolproof. Sometimes you can't view attached images using the app (it appears as a "broken" image), which forces you to use the "Open in Browser" function.
Also, as mentioned if you are not a Silver or a Gold member, the app is of quite limited use to you.
Finally, as others mentioned, if the app is not supported on your mobile device, well, out of luck. (Probably the main ones missing out here are the Windows Phone users).
Before I moved to a smart device I had been asking for a mobile version of AFF to be refined for ages (and mainly because my attempts to access AFF on the road was via old, slow GPRS packet rather than 3G). I'm glad there's a mobile version but admittedly the UI painfully needs work. I'm not sure how it can be done - the last time I discussed with a mod about the mobile version of AFF, they said it was just a skin - there was no explicit version (or backend) of the site which renders AFF into a mobile version. vBulletin simply supplies a "mobile skin" which you turn on with a switch. Obviously, it's not the best out there (or at least when rendering AFF).
One of the problems I had in the old days when I wanted to access AFF mobile a lot more (the app version was in its infancy then) was you would get the desktop version of the site but it would be extremely difficult to get access to the mobile version (because you had to find a specific drop-down box; apart from the fact that the mobile version was only for Silver and Gold, so you needed to sign in). One of the suggestions I had put forward was there be a link or something (maybe near the top, maybe in a button, or just a separate page, e.g. [noparse]www.australianfrequentflyer.com.au/mobile[/noparse]) so those that wanted to access the mobile version could do so easily. Maybe there could be a similar thing here (most company websites have an option somewhere on the page to switch between desktop and mobile versions) - the setting is stored in a cookie (which, hopefully, for most people will be persistent enough so they can browse AFF smoothly in at least a few sessions). That said, AFF is pretty much running off the vBulletin platform with not much else running off the side (from what I can understand)....
On my Samsung Galaxy S3 I use Dolphin Browser (rather than the stock supplied Internet) which allows me to change user agents (so I can force all websites to render as if I were browsing through a desktop). As mentioned, Chrome offers the same thing.