Heh - welcome to every debate ever between CAMRA members and the non-believers....
Without going into too much detail - as someone who has grown up with pubs that have cask-conditioned beer and force-carbed keg beer side-by-side, sometimes with the same beer on - I can tell the difference every time. In general traditional British styles just don't suit kegs in general, the mouthfeel ends up all wrong. Nitro is less bad than CO2 carbing, but still not the same. And it's not just with beer - I've done blind tastings of sparkling wines and can easily tell the difference between the bottle-conditioned, the Charmat process (effectively secondary fermentation in a secondary tank before bottling under pressure) and force-carbed wine. The bubbles are just different, even when the bottles have been cellared a while.
Whilst the fact that the yeast is distributed throughout the volume of the liquid and is producing "microbubbles" of CO2 with a huge suface area : volume ratio that dissolves very quickly and uniformly is part of it, you also have to consider how it comes out of solution. All those yeast cells, dead or alive, produce huge numbers of nucleation points, to form lots of small bubbles, even if most of them are dropped out. I don't really buy the impurity argument from a bubble perspective, but the presence of oxygen will certainly affect flavour.
Also - sparklers.
Hello all - I just got my score sheet from a competition and one of the comments was "carbonation is more bubbly than creamy", which is fair - the beer can feel almost soda bubble-ish on the palate at times.
As a Brit who drinks cask mild maybe once a month on average - I'd say the judge is absolutely right to pull you up on that. To be honest, mild at 2.3vol and 45°F (7°C) with soda bubbles sounds rather unpleasant.
British styles are all about balance, and skewing that balance even slightly one way or the other makes a big difference. Particularly with excess carbonation, which not only affects the mouthfeel but also puts carbonic acid into the beer and skews the flavour that way. Which is particularly noticeable on a "slight" beer like mild, particularly if you're killing what flavour there is by serving too cold.
The official recommendation is to serve cask beer at 12-14°C (54-57°F) - personally I like to start my bitter at 9-10°C (48-50°F) so that it warms up through the sweet spot as I drink my pint. Mild I'd probably want a touch warmer, maybe 11-12°C (52-54°F). Whilst I've had cask mild come out so lively it didn't even need a sparkler (!) I'd guess I'd expect it to be 1.7-1.8 vol on draught, and aim for 2 vol in bottle as bottles always seem to need a bit more?
If you're doing another one - partigyle it off a big dark beer, you can save the big beer for Christmas whilst still having something to drink immediately.