IBM made the Hollerith punch card system something of a business standard in the 50s and 60s - and I've dug up one reference to them being used by a police service.
and, from http://www.firethistime.org/fearusgovt.htm (quoting a BBC documentary)
In a savage irony, Jewish refugees escaping Nazi persecution, many of whom later moved to the Israeli 'homeland', are now firmly allied to the US - the same country that may have partially contributed to their terrible fate in the first place. The American IBM corporation was instrumental in providing a prototype 'punch card' system the Nazi party to collate information on the Jews. This early computer alllowed high speed information processing of the 'Final Solution'.
As to advantages, well, the ability to more quickly re-run a task repeatedly with different parameters is the obvious one.