As far as pilots are concerned...
I remember the barney the postie had with pilots as stuff was leaving our place once. Postie wanted to duck in to drop off mail, pilots had the lights flashing so they were the bosses. The police that were there burst out laughing though and just let those guys yell at each other.
Basically, follow their instructions. Don't overtake unless there is a whole lane (i.e. pretty much need dual carriage way) or they wave you through. You're not sure what the next move is, so they might be planning to block off an intersection or something ahead and the last thing they need is cars weaving in and out.