Having tried the BT sport app for several days on my Galaxy Tab 2 10.1, I have found an identified problem.
If I watch video on demand snippets, the picture quality is great, no stutter and no break up.
If I watch any of the 3 live channels, then the picture quality starts great. then goes blocky after 30 seconds or so, then around a minute onwards I get a stuttering picture. If I stop the stream and start again the cycle repeats itself.
I have tried this dozens of times over the weekend and I don't know if it's device specific.