The most common problem has been the issue how people's birthday has been registered. Often the birth year has been registered with two digits only, either assuming when designing the routine that it is not important exactly how old people are, or assuming that everyone is less than one hundred years old. In the late 20th century (before the year 2000), everyone alive at the time was born in the 19th or the 20th century.
In several countries, especially in Europe a national identification number was introduced (often in the 1950s) including information about the birth year, with two digits. The largest effect was that people 100 years old or more were mistaken for small children.
When handling the year 2000 problem, measures were sometimes done to avoid this problem, e.g. modifying the national identification number, even if the same problem already existed, the year 1900 problem.