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Azurewood,
Is Robert Scarth, the 19th C Kirkwall solicitor, who was factor of the Traill Estates on Rousay, when the infamous Rousay Clearances took place, related to this family?

Spittalhall, the Robert Scarth you're speaking of is my Great Great Grandfather. 

Robert wasn't a solicitor; he was an agent of the Union Bank, a factor and a landowner. 

Robert was the factor for the Laing family and also the Traills of Woodwick between 1852 and 1873.  I understood that the main clearances on Rousay were in the 1820s (before Robert was factor) and again later under General Burroughs after Robert had retired. 

I have not managed to link William Baikie Scarth's ancestor into the Binscarth Scarths but given that Orkney is relatively small it is probable that he does link in somewhere.

I see James Irvine Robertson mentions a John Scarth in his journal of 1851, but it's not clear it's John Stuart Scarth, and probably isn't; but I'm wondering.

Hi, I know I'm late coming in on this but I can confirm that the John Scarth referred to in James Robertson's journal of 1851 is not the one you are looking for. 

"Tuesday 18 March 1851
...Dined with R and John Scarth at Mrs Patersons. Home at half past 7."

The R Scarth is my GG Grandfather, Robert Scarth of Binscarth (1799-1879) and John is his brother, the Reverend John Riddoch Scarth (1806-1871) minister at Sandwick in Shetland. 

James Robertson would later, in 1859, marry Robert and John Scarth's niece, Harriet Logie, the daughter of the Reverend William Logie and his wife Elizabeth Scarth (Robert and John's elder sister).

Later still, Robert Scarth's grandson Colonel Henry William Scarth would marry Mary Beatrix Robertson, the granddaughter of James and Harriet Robertson through their son Duncan John so the families continued to be closely related.