What due-diligence standards, such as prior criminal convictions, are there for investment immigrants to Portugal?

When applying for a Golden Visa, one of the required documents is an updated criminal record issued within three months prior of the submission by the country of origin or by the country the applicant resides in (if different) and if he has resided there for more than one year. The granting of a Golden Visa will also depend on the absence of a conviction for a crime which in Portugal is punishable by a sentence of more than one year; Therefore, it depends on the type of crime that lead to a criminal conviction and if that type of crime is punished in Portugal with a sentence of more than one year.

According with Portuguese Law no. 23/2007, the article 77º nº 1 paragraph g) foresees that in order to be able to apply for a temporary resident permit (note that the Golden Visa card is a temporary resident permit for means of investment), the applicant cannot be previously convicted for a crime that in Portugal is punishable with deprivation of liberty for more than one year. So in your case, if you were convicted for a crime that in Portugal is punishable with deprivation of liberty for more than one year, you are not eligible to apply for a temporary resident card. If not, you can freely apply and a temporary resident card will be granted. Note that your criminal record will be requested by the Portuguese immigration office, either the one for Colombia or for a country that you would be settling in for more than one year.