The guidelines for Finns wanting the same permit into New Zealand requires applicants to be 'of good character':
"Under sections 15 and 16 of the Immigration Act we will not grant you a visa if:
you have been convicted and sentenced to imprisonment for 5 years or more (this applies even if any of your offences have later been taken off the record)
in the past 10 years you were convicted and sentenced to imprisonment for 12 months or more
you are subject to a period of prohibition on entry to New Zealand under section 179 or 180 of the Immigration Act 2009
you have been deported or removed from New Zealand under any enactment (whether before or after the commencement of the Immigration Act 2009)
you are excluded from New Zealand under any enactment
you have, at any time, been removed, excluded, or deported from another country
you have been involved in terrorist activities, or belonged to or supported any organisation involved in terrorist activities
it is believed you are likely to commit – or to assist others to commit – criminal or drug offences, or an act of terrorism, in New Zealand
it is believed you are likely – due to any international circumstances – to be a danger to New Zealand’s security or public order
it is believed you are associated with an organisation or group that has criminal objectives or is engaged in criminal activities and for that – or any other reason – you’re considered to be a threat to the public interest or public order of New Zealand."
They likewise carry out checks on all applicants, however unlike Finland, they aren't kind enough to ask your permission for the checks
So here's hoping it's the same, or similar criteria for New Zealanders wanting the permit for Finland.
My appointment is with the embassy in a couple weeks, and I've been advised waiting time is 1-2 months.