The methods are thorough, complicated, and account for almost everything, no doubt about it.

This conversation however, brought into my mind an article or a lecture which I've read/seen long ago (I can't remember) about "noise" and filtering any data.
It was about how despite "filtering" any data as much as possible for example, we'd still end up with some "noise" left which we usually try to ignore and throw away. But when looked at and reassessed as part of the bigger scheme of things, it proved to be an integral and essential part of reality. And without them, the actual "interesting" data wouldn't give the whole picture or make much sense.

(I'm sorry I couldn't find it, and I probably explained it in a little messy way to make it short)

What I think @agmoore was partly talking about, is that filtering that happens by the triger mechanisms and all other consequential filtering which takes place, could be omitting some interesting "stuff".

@lemouth, you maybe needed to include more info about what "gets ignored" and why, and why the low energy events are considered not interesting.
"Minimum bias" also, is just that, "minimum".

Going into the very interesting brain analogy and the filtering of our sensory. Such "filtering" does an amazing job to give us useful data for "our needs" but it's far from the reality, in the end our perception is very limited and we detect a very limited info of what's "out there".

To sum it up and to clarify, do you think there are limitations in how the data is collected/processed in LHC that can make a "big difference" of the results?