Welcome to rootschat
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Gosh, think folks are struggling on this one as much as you are given the discrepancies in the parents names.
As said, marriage records are often more accurate as person giving details of parents is still alive, but, even marriage records can end up wrong if that person cannot read and has not realised a mistake has been made in the written version of the details they gave verbally. Or, person has given misleading info either because they a) don't know their parents names b) choose to.
Can I assume the marriage details posted above are from the Statutory Register rather than the Catholic Register? If yes, have you checked the Catholic Register entry too for any potential additional info that may have been captured? I've done a general index search on scotlandspeople and there would seem to be one, albeit possibly with slight differences in spelling (I used some * wildcards, but narrowed to the 2 St Mary's chapels in Dundee area and the year of marriage).
Also, have you checked witnesses on marriage and informant on deaths? If related, then finding the witness in the Census might help. Not often, but sometimes, a County in Ireland is captured in the census. Grasping at straws, yes, but can be worth checking.
As we are grasping at straws, and to prove that sometimes Counties of birth in Ireland are captured, I will throw a few more suggestions for you to check further. In 1861 Census for Dundee there is a Patrick Smith lodging with a Kelly family. His birth county is noted as Cavan. Now whilst he may be a different Patrick from the one Mary was married to, interestingly, there is another lodger in the same house. I am working from transcripts, so haven't seen original, but she is an Ann Curran
ts, birth County Sligo. I wonder if original says Currants or Curran? Your post above notes Mary had middle name Ann. All speculative thoughts, but at least some things to consider and check further. Going against it though, is Mary's 20 yr old daughter in the 1881 census. Considering her, there is interestingly a record for Portaferry, County Down, Ireland albeit 1871 (mistranscribed ?) for an Eliza Smith born to a Patrick Smith and Mary Ann Curran. Again, 1871 could be correctly transcribed and it just be a totally different couple with same names. And indeed I've found more births beyond 1866, so this seems another non runner.
Picking up on the Finnan surname Mary gave for her mum at time of marriage, there were a number of Finnan's living in Dundee, so quite possible Mary, if the daughter of a Finnan female, knew some. Co-incidentally, David Guild Nicoll's wife Isabella's sister-in-law had a sister married to a Finann.
scotmum