Does the speed of opening of a bottle of wine influence its flavour?
This seems to be a myth based on the idea that wine can be 'bruised' by popping the cork or handling the bottle roughly.

'Dr Vinny', Wine Spectator Magazine's advice expert, has this to say on the subject:


  Someone asked whether or not making a cork "pop" when you pull it will bruise the wine. Others have also asked about bruising in relation to decanting. I've never had a wine that was fine one moment and damaged the next because of handling, and can safely say that bruising wine is a myth.


Source: http://www.winespectator.com/drvinny/show/id/5369

and also:


  A wine does not get “bruised” by moving it around. And let me address some other myths, such as that wine will bruise if you make a cork “pop” or bruise if you decant it: no and no. Outside of smashing a bottle on a concrete floor, there is nothing I know of that will take a perfectly fine wine and damage it in one movement.


Source: http://www.winespectator.com/drvinny/show/id/40542

You are more likely to have a problem with an old, crumbly cork falling into the wine than some pseudo-homeopathic magic going on when the cork pops.