To answer a couple of your questions without getting too longwinded about it:
As to the nature of climate data itself, data sets which are of sufficient size are generally of questionable quality, and data sets which are of known high quality are generally too small to be useful. Climate folks use this as an excuse to do all sort of tricks, including using mostly models instead of actual data, and (my favorite) using a relative handful of actual measurements to create (infill) a whole lot of basically fictitious data points. That's why I always ask the question that I do, because I don't think people realize how little actual high-quality data is really being used here. You say that "Modelled or infilled data does not count", but in climate science it seems to count for an awful lot!
As to the nature of the adjusted data set that I reviewed, IIRC the rationale being used there was as follows. If you take a set of temperature sensors which are in relatively close proximity to each other, and one of those sensors starts showing a noticeable shift in temperatures, then the other nearby sensors should also show a similar shift. If they don't, the argument goes, then you can assume that the original sensor is suffering from some kind of anomaly and needs to be adjusted to correct for that. For example, perhaps that station had been moved a bit, enough so that its temperature-sensing characteristics had inadvertently changed.
Even if you assume that making such an adjustment is valid (I've seen well-reasoned arguments that it isn't), then the next question is how much to adjust. And that in itself leaves a whole lot of room for error. But none of this really applies to what I found.
The data set I reviewed was temperature data from sensors located all over the world; I was primarily interested in my local temperature history, though. When I downloaded all of that data I fully expected to see adjustments that seemed to at least be reasonably in line with what the computer algorithm used to make those adjustments was trying to accomplish, as explained above. But when I did even the simplest possible analysis (subtracted the raw numbers from the adjusted numbers) what turned up instead was quite surprising. Working from memory, this included:
1. Adjustments that were pretty much identical no matter where the temps came from or when they occurred. The same adjustment values were used for stations all over the world - Cairo or Anchorage, new data or old data, it didn't matter. (I didn't review all of the stations, though, just spot-checked several of them.)
2. The adjustments came and went, repeatedly - now you seen them, now you don't. If, for example, this was supposed to correct for a potential station move, then that implied that the station moved from point A to point B, then back to point A, then back to point B again, then back to point A, and so on.
3. The adjustments were always positive, never negative. This means they were adding considerable heat to all of the records.
4. Adjustments for winter temps were different from those for summer temps. For example, IIRC winter temps were adjusted upward by a full degree while summer temps were adjusted only by 1/10th of a degree.
There's probably other stuff, too, but I don't remember all of it. Other people out there also looked at this data and came up with other issues. Some even went so far as to look at the program code itself, and IIRC they said that no matter what the nature of the data was that you threw at it, it was always going to add considerable warming. As for my local temps, the raw data showed a small but apparently very real warming, while the adjusted temps showed a far more dramatic warming.
Being a computer guy myself, my take on the situation was that, at a minimum, the computer algorithm had been allowed to run roughshod all over the data. And at worst this may have been an intentional attempt to deceive - adding warming which wasn't really there.