For me the app seems pretty good but I have some ideas for improvements...
Stream bitrate quality options. As YouTube does maybe an option to select higher or lower quality streams to suit varying broadband speeds
In the fixture lists highlight which matches are live on btsport
Have an option to set alerts for the sports you're interested in so you don't miss any. Ie get a push notification to your ipad or android whenever a premiership match is about to kickoff live on btsport