Hi Bob, just been reading up on King's Square and how amazing it is, but there was mention of on-going construction work and beware of pickpockets operating, both day and night! Perhaps no different from many other cities.
Kongens Nytorv is very nice, but amazing would be too strong a term. However, there is major construction work, so edge along to Nyhavn instead.
The pickpockets are not too much of a concern really. Just be aware you are a foreigner abroad and it is no worse than any other European city.