I know something about how the Nordic countries assemble their records and there it seemingly is a case of if someone tests positive for Corona virus then that is a recorded case, active if no antibodies found but inactive/recovered if symptomless but with antibodies. In some cases/countries all infected individuals were monitored to the end of their illness (while in quarantine/isolation/hospital). Deaths are recorded as being due to Covid if the person is Corona positive and being treated and/or recovering from from the illness - recovery only being declared once all symptoms have disappeared. There it is accepted that some cases will go totally undetected which is why they also assume/indicate/publish "for discussion/information only" an assumed grand total of infections over and above detected ones. These countries have from the beginning tested all suspected cases plus hospital admissions plus health care staff and care home residents and staff. Some of them have provided testing on demand generally, well beyond the above list for routine testing. Further, some of them currently test arrivals from abroad and also again within a week of arrival (local residents only). Because there has been lots of comprehensive testing from the outset I would easily accept Nordic records as complete and entirely reliable. Incidentally, Greenland falls into the same category although not a Nordic country.
I am insufficiently familiar with the regime used in Germany but I would be inclined to think their records are quite thorough. Also, it would not surprise me if countries such as Czechia, Slovakia and Slovenia and even Portugal are pretty good or at least close to being beyond major criticism. Some Asian countries I would expect to be just about as good as it gets. There will be other countries possessing very impressive accuracy.
Every record should be subject to scrutiny but not to the point of pedantry - they should meet all reasonable expectations but focussing on the last digit's precision is not reasonable except for example where case/death numbers are very low. On records, the UK's failure centres mainly (but not only) on not having tested anything like rigorously enough throughout so a lot of information/knowledge was permanently lost, that loss is irrecoverable and estimates will have to be resorted to. The credibility of the estimates will be something for discussion/debate, probably for years to come. What we here on AB think in these matters will not matter anywhere beyond AB.