I have a few things to mention about Picking Battles and Natural Consequences - however I would like to be clear that this is what I know of the theory, I am often rather rubbish at putting it into practise.
Picking Battles - there are many things, like silly noises, which do annoy you, but in the bigger picture don't cause any harm. If you heard someone else's child doing it, you probably wouldn't notice or care and certainly wouldn't judge the parent for it. Yet somehow, when it's our own children, it is a button pusher. I'm trying to make more effort to ignore some of the things like this, which really don't do any harm and aren't a big deal.
Deciding what falls into this category isn't always easy, as some sibling bickering does and some doesn't, sometimes leaving them to it teaches negotiating skills, but sometimes you have to intervene to ensure the smaller sibling isn't totally pummelled.
An occasion where I noticed this, was when DS1 and 2 other friends were playing at the beach, 3 frisbee rings, 3 boys. They kept arguing over them and us parents were just about to intervene, to remove them all or enforce a 1 boy, 1 frisbee rule, when the boys started playing a game which involved each of them taking it in turns to throw all 3 frisbees at once. It was a very close run thing but they did make a game which worked, which wasn't what we would have chosen and enforced, but was how they wanted to play. Everyone was happy with no punishments or arguments (a rare event).
Natural consequences is probably even harder to work out and enforce, I consider natural consequences to be things like - refuse to get dressed in time, not have time to play x before school. However there are many, many grey areas, like refuse to wear coat means get cold, but I would carry coat and let them have it once they say they're cold, rather than freeze completely. I would say, but we have to cross this road (or similar) before putting it on, so there is a clear sense that if it's refused at a certain point, it's not instantly available at another, but without being cruel (in theory).
It's also about making the consequence fit the crime, so scooting too fast and without paying attention, means the scooter won't be taken out with us for a while, because they need to understand it is dangerous for themselves and other road users, so I can't let them do it, unless it's done carefully. Removing TV watching privileges for irresponsible scooting would probably seem unfair and irrational to the DC, which makes it harder to learn the lesson from. As a normal, responsible adult, I understand that if I left my shoes out in the garden, it means I have wet shoes and have to wear another pair or not go to the activity which involved those shoes (so no gym if trainers are wet), I would not understand if it meant I couldn't watch TV on Saturday night, as this has no relation to my shoes wet/dry status.
I think How To Talk So kids Will Listen has better examples of this (I have read it and do agree with it, despite an inability to put it into practise). My mum was a HTTSKWL parent and, although I love her dearly, I get very irrational when people try to ascribe me feelings I don't have (which she did do according to this book's teaching), I agree recognising your DC's feelings is a good thing, but hate the way the book instructs you to tell them you know they're angry/frustrated/etc, when this isn't always the case. I definitely agree with trying to apply empathy, to understand where they are, but telling them they're feeling certain things might be counter-productive.
Although I worry that I shout too much, I'm also not convinced that constant understanding and unconditional parenting, turns out utterly happy, confident, perfect DC. I think it's far more fair to say we all just mess up our DC in slightly different ways, according to our parenting style (based on the fact me and my sisters are all slightly screwed up, but in different ways, by semi-unconditional parenting).
Our biggest battles have always been when I've tried to push something, which I think they should be doing, but they aren't developmentally ready for. I think walking instead of buggy, potty training and general independence skills are places where we've had huge ructions trying to do what society thinks a 2,3,4,5,6 yr old should do, and then they've just gone ahead and done it with no problem a few months (years/ tears) later.