OK.....I'm a piano tuner. Been doing it for 25 years and I currently tune 3-5 pianos a day five days a week, sometimes more. I have about 2500 churches on my account list and probably another 800 individuals. I probably tune around 1000 pianos a year plus all the repair stuff.
A quick response to the things I remember from the previous posts.
1. You pull the upper octaves
sharp according to a electronic tuner, not flat. It's called even-tempered tuning and the amount of sharpness needed varies. I've seen pianos that didn't need to be stretched much but I've seen others that needed to be stretched as much as 1/4 step by the time you got all the way up.
2. You don't pull an adjacent string out of tune when tuning the next note that uses the same string. They do not slide around the hitch pin. I do this all day long every day and I can say with certainty that this doesn't happen. If it seems to be happening, there's some other mechanism at work.
And the reason they use a single string looped around a hitch pin is because otherwise you have to tie a loop in the end of the string. Piano strings don't come cut to length with loop ends. If you need a loop you have to make it and it's a bit of a pain. Much easier to do it this way.
HOWEVER.....there are pianos that use single strings for every treble string. They all have individual loops on their ends. It's not real common but I see it. Oh, and also....the piano wire is not the same throughout the treble unisons. It changes guage about every 6-8 notes.
3. Why do some strings not stay in tune? Well besides the fact that pianos are creations of Satan sometimes,

there are several possibilities.
Loose tuning pins is a possibility. As was said earlier, you can replace them with a larger pin. Someone competent with tools could do this but where are you going to get the pin? And how do you know what size to get even if you knew where to get one? And you can't buy one anyway....you can buy a box of 250 for about $80. And to change the pin you'll almost always have to replace the string so then you have to have the right string.
You can also drive them in a little deeper to get a bite of some unused pin block. But I would consult with me or a tuner for some specifics before doing it. You could screw-up.
You could also have a string that was replaced and is still stretching just like new guitar strings do. Only a piano string
can stretch for a freakin' year! Drives me crazy sometimes.
You can sometimes just have a string that sucks. You know how a guitar string sometimes won't stay at a particular place but will invariably jump up or down? Well, same thing. There's some things that I can try but sometimes it's just a sucky note. Pianos aren't perfect and they all have a note or two......some pianos have lots of them. You can even have a string that has prominent upper harmonics or partials. When they're strong enough the note will never sound right because you always hear two notes.
4. Can you tune your own piano? Granted, I'm a tuner and so you might think I wouldn't answer something like this honestly. But come on, none of you guys live where I'm gonna get the tunings so I have no motive to lie. So.........you can probably keep a problem note in passable tune if it keeps going out between tunings. And the fear of damaging a piano if you dare to fool with it is somewhat overstated. It is, after all, simply a mechanical device. A wooden one, but a mechanical device nonetheless and they don't just turn to dust if you hold your tongue wrong. But most of the tools needed to work on them are specialized and not available outside of piano supply places and many repairs simply can not be done without the proper tools.
And when it comes to regulation or voicing.....well I know professional tuners that aren't any good at regulating and many who simply
won't do voicing.
So minor tuning of a few notes......you can probably do.
As for a complete tuning that ends up sounding good? Not a chance.