A decent app would require some kind of accessible API for the GameDev.net site, and last I asked, there wasn't any kind of answer. Maybe a staff member can say whether or not such an API exists (and is publicly useable, unless, of course, the staff decides to make their own app).

Cornstalks is right, less writing a custom browser for mobile devices to properly mimic HTTP connection states and parse the HTML there just isn't any way to interact with the database of a site unless the provider / creators specifically provide one (eg php / asp files that talk in some usable api such as json, xml or even a custom format.)

The problem with providing a public API that allows something other than the website to access the information of the site is that it gets increasingly easier for smart developers to effectively "rip off" the content of Game Dev. That is to say if Game Dev is like "this is how you log in" "this is how you get forum threads" "this is how you post to the forum" and so on... It is just that easy to make an app that uses Game Dev without crediting this site for the content in which it leaches. Along with the fact that Game Dev general access is a free service to the public with attempts to monetize through advertisement, GDNet+ subscriptions, marketplace and help wanted commissions this would completely defeat the profitability potential of the service.

So all in all I would say that Game Dev should explore the mobile app idea, but until they do perhaps you should look into correcting the issues that are preventing you from logging in. Game Dev persists log in credentials and sessions through cookies, if your mobile device is attempting to store a login session with a cookie it is entirely possible that the Game Dev server is actively refusing you at another location if your IP changes. (This is actually a good safety design that stops quite a bit of "session hijacking" hack attempts). This may be very difficult to work around on a mobile device and the simplest fix is log out before you move to a new location and while you are physically in motion stay logged out until you need to be logged in. At which point, stop moving, log in, do your thing, log out and get back in motion. Set Game Dev NOT to keep you logged in, and clear your internet cache / cookies regularly and it should get better for you.

P.S.

I do mobile app development and Cloud / Web Service development professionally and would be interested in doing something along these lines. If the Game Dev gods happen across this post and are interested feel free to contact me, to the OP if you get permission from the Game Dev staff to do something and need some help feel free to contact me. Please note that my participation in something that relies on Game Dev content or technology 100% depends on Game Dev's permission to do such. eg: I'll help you fix the problem with your mobile if I can, or I'll work under the permission of Game Dev but in no other way would I use Game Dev services or content.

What would be the goals of such an app?