Joshaw, there is no doubt that this app design is very elegant and beautiful, but I believe there are a few limitations/problems which may arise. Here's my opinion:
0.1. GIVING A USER HIS/HERS MOBILE/ACCOUNT INFORMATION: You have achieved this, though I think there may be some problems (read from 1. onwards).
0.2. TOPPING UP & ADDING GOODYBAGS: Achieved.
0.3. SPREADING GIFFGAFF TO OTHERS AS EASY AS POSSIBLE: Achieved; your design (minus the orange box) makes this part intuitive and efficient.
0.4. BEING CONNECTED TO GIFFGAFF...: Achieved. I love the notifications section; could give the option to enable notifications to appear in the status bar too.
0.5. ENSURING GETTING HELP...: Achieved.
1. HOME SCREEN: The 'home screen' looks great on the GNex screen, as I'm sure it would on any large displays (w/ high ppi e.g N4/SGS3); but what about people with more budget devices with smaller displays (lower ppi)? The elements of the design with smaller fonts like the goodybag information on the left hand side may be very hard to read or select; some of the elements such as the orange box (containing the 8 links) and the circle (my giffgaff) may overlap if not scaled correctly to accommodate these displays. This may be averted by implementing a 'menu' with larger text (which may be the purpose of the column of three squares on the top right) to select the 'tools', 'spread', 'community' etc.
2. HARDWARE VARIATION: I'm pretty sure this app would run smoothly on a GNex or any phone with a faster processor (ARMv7/Krait/1GHz+) though it may be laggy on a device with a processor running on the ARMv6 (with low clock speed) architecture for example. The reason I think it would be laggy is because of the complexity of the app, it isn't just displaying the giffgaff website in a frame or something similar.
2.1. DATA SPEED: Slow data speeds could be a problem, although I think it would generally be fine (excluding accessing the community/help sections).
3. TOP UP PAGE: Get rid of the orange box when you enter the top up section, and use the 'menu' icon (the three dots) as a way to access the links in the orange box (the orange box isn't really needed in this section). This would save a lot of room - very useful for phones with smaller displays.
4. SPREAD/COMMUNITY/HELP/NEWS: I'd recommend the same as I did for the top up page for these sections. I love design of these page (minus the box at the top), in particular the community section. However, when one of the options is selected, like the 'search for answers' (great job for introducing that, I'm a strong advocate of searching before posting 🙂 ), will it open the default browser (with the appropriate URL), will it nest the browser around a frame within the application itself or will you design a new way to display this? If you could design something new (which will no doubt be very aesthetically pleasing like the rest of your app) it would be brilliant.