Back in the 'good old days' of connecting between T4 and T1, there was a phase where my bag mis-connected more often than not. Then there was the time that my bag was literally torn down the middle and leaking clothes all over SIN baggage claim. Whenever I've made a claim, BA has dealt with it swiftly.
Since T5 has opened, I've (touch wood) only had 3 bag misconnects and no real damage to speak of.