Calcium sulphate scale can form too. When copper boilers are in contact for a very long time with water that does not scale they will become coated with a nearly black layer of CuO. This is a good thing, because this layer is thin and prevents further oxidation of the copper underneath. Constant descaling removes the oxide layers and then more of the surface becomes oxidised to form a new protective layer. Calcium sulphate is slightly soluble and will gradually dissolve if you use sulphate free water, or better still calcium and sulphate free water. However, to me, it has a slightly unpleasant taste until it is gone. However, all sulphate hard water has this taste.

I removed a sight glass two days ago. It was used before I got it with terrible local water, but the deposits were entirely gone because I only use 1.0 mM potassium bicarbonate in distilled water for espresso brewing. (100 mg/litre) The problem I had was that the silicone seals had cold flowed around the washers between them and the nut. I grabbed the flowed material with a dissection kit tweezers and pulled it out. Then I wrapped the tube with tape and it came out quite easily. I wore heavy gloves because glass tubing can break! With some coffees and roast level I cut the potassium bicarbonate to 0.5 mM, 50 mg/litre. It is amazing how perfect a boiler looks when used with that mixture even after several years.

Could I just fill the boiler with distilled water amd then peave it there for two weeks, without using the machine? Would that give the desired result?

If you do not use the machine the distilled water will quickly become saturated with calcium carbonate (or sulphate) and then no more deposit will dissolve. If you use water without calcium for a long time the slight solubility of calcium carbonate (or sulphate) will result in its slowly dissolving. When you use the machine with Ca free water you are constantly replenishing the water and the Ca gradually is lost, it is especially fast with calcium sulphate because it is more soluble than the carbonate in pure water.

One more thing about the distilled water. I really like your approach with distilled water for making espresso. But I live in the netherlands and distilled water is not something wich is sold for consumption like in the usa (because of solvents it is said). Would it be a bad idea to use this kind of distilled water for the purpose described above without making drinks for consumption but to get rid of the remaing scale in the boiler?

I cannot see any reason not to use distilled water soaks to get rid of slightly soluble things. You might want to heat it up and let it stand a while. With calcium sulphate you might want to let it cool before draining.