I'm sorry, but I don't like this UI at all. It looks foreign on the iOS as if it were designed for some other device and the ported over. Such neglect for the consistency with a native look and feel is not a "fun experience", it's really quite annoying. My iPhone is not an empty canvas for you to drop an arbitrary UI style on. It comes with Helvetica and a whole bunch of well designed controls. I insist you use them.
Custom UI is common in most apps - this isn't a bootstrapped app or something quick and dirty. Why would they use the default/built-in/native UI design?
Now, if you meant it's foreign because of the design style, then you may have a point. iOS apps tend to designed with elements such as textures, gradients, drop shadows, inner glow/shadow etc. While Android tends to be flat and borderless.
There were parts where it definitely felt Android/Flat (icons), other parts felt iOSish (buttons).
The custom alerts were definitely a nice touch - don't see alot of apps with custom alerts. I didn't mind them - but some may not find it as impactful as a 'real' alert (it's like a warning usually comes in red, but it's now in blue. Just doesn't carry the same weight/feeling.)