Also, why would Elisabeth Snedden be listed on the census with her maiden name? Is that how it's done in Scotland, and she didn't take her husband's name? Or do records require that the maiden name be listed?
It's quite common. In Scotland, a married woman did not change her name legally on marriage. This is why you mostly get the mother's full name in the baptismal records, and why married women's death certificates are indexed under both their maiden amd their married names. 'Mrs' was an abbreviation of 'Mistress' and carried no indication of the woman's marital status, though it often indicated a degree of respect in the social pecking order.
Thus in the song 'The Laird o' Cockpen', which tells the story of the Laird's attempt to woo his neighbour's daughter Jean MacLeish, there is the line, 'Gae tell Mistress Jean tae come speedily ben, she's wanted to speak wi' the Laird o' Cockpen!'
You also get baptism records like this, from the parish of Rothes, '1748, September 11th. William lawful son to Alexander Leslie of Balnageith in Burncrooks and Mrs Anne Duff his spouse was baptized.'
Sorry for all the dumb questions, this is my first attempt into Scottish research, and just don't know all the "rules" yet.
I've read some where that the only dumb question is the one that isn't asked

His death certificate shows that James Kennedy was born in New Caron/Carre(?) Barr, Scotland, in 1842, but I have not been able to find such a place. Do you know where this might be?
FreeCEN
http://www.freecen.org.uk/cgi/search.pl lists in the 1851 census at 17 Reid Street, Bridgeton, Barony Parish (i.e. in the city of Glasgow) the family of Peter Britten, 78, born Ireland, including his wife Agnes Duffy, 67, widowed daughter Mary Kennedy, 34, born Sanquhar, Dumfries, and four Kennedy children, all born in Bothwell; James, the eldest, is 9, so born 1841/2.
In the Roman Catholic baptisms on
www.scotlandspeople.gov.uk the index lists the baptism of James, son of James Kennedy and Mary Bretain, in St Margaret's, Airdrie on 2 January 1842. There is also a marriage record of James Kennedy and Mary Br*t*n. I didn't go beyond the index.
The 1841 census on FreeCEN lists at Carnbroe Iron Works James Kennedy, 26, born Ireland and Mary Kennedy, 19, born Ireland.
So in spite of the discrepancy in the birthplace of 19-year-old Mary in 1841, I think it likely that your James Kennedy was born at Carnbroe Iron Works in the parish of Bothwell, Lanarkshire, to parents of Irish origin.
You'll want to have a look for yourself at the above sources, and to look at the original documents on the Scotland's People web site - it's pay-per-view, but modestly priced compared with many parts of the world.
I imagine this will help?
PS They would not recognise Carnbroe now
http://www.geograph.org.uk/gridref/NS7463. The iron works were built in 1838, just in time to attract your family to come over in search of work. There's quite a bit of information online about Carnbroe Iron Works.