I added to our Castle Game Engine two very useful features for remote debugging:
You can register custom event on the ApplicationProperties.OnLog list. This allows to observe all the CGE logs (including warnings).
For example you can send these logs to a remote server. This CGE example shows how to do it. It assumes you have your own server with a simple PHP script somewhere (the PHP example script is also included in the sample code).
You can integrate your mobile game with TestFairy. It is a mobile testing platform that allows to distribute test applications easily (on both Android and iOS). It can also (optionally) gather logs from testers, their device details (phone model etc.), and even record videos of their playthrough.
Note that TestFairy is a paid service. But they also have a free plan (Essentials Kit).