A recent experience, came into T3 with AA going to T5 BA. I was down to 1hr10 minute connection, as the inbound was delayed.
At the exit of the aircraft I was handed an orange "oneworld express connection" paper sleeve and told to keep it visible at all times, along with instructions on where to go by the AA agent.
Once at Terminal 5 another BA agent with the flight number/destination, was waiting for me and escorted me through security (a distinctive line for this).
I'm not sure if this is for all oneworld connections or only AA/BA/IB ones. The overall process was efficient, although falls short of what AF do when you are on a 45 minute connection at CDG (bring a car to your inbound aircraft, drive you immigration and subsequently escort you right through to the gate). I'm not sure why oneworld do not do this, maybe BAA is opposed to the idea?
A couple weeks ago my inbound AA flight was late, leaving me with only about an hour for a connection to BA in T5. After exiting the jetbridge, a BA agent with a large sign reading "connections" asked me my destination, then my name, and handed me the orange high-visibility hashed card with "priority connection" on it. She didn't tell me to keep it visible, but she did say "Run to T5! Run!"
At the Flight Connections bus, the card had no effect.
At T5, I held the card up but nothing happened. I went to the FasTrak line, then security, and no one cared that I had the orange card. I got to the gate just after boarding started, but didn't see the point of the card.