edit: removed for potentially being misleading.
But they validated their results with a second step, the "pseudotype neutralisation assay". This test is highly specific for SARS-CoV-2 - as I understand it, they essentially introduce the virus to the hypothetically immune blood samples and then test that it is indeed neutralised by antibodies.
So, I think this Scottish serology test is pretty robust and accounts for these issues with cross-reactivity and specificity of the testing. In addition - they used a control sample from December 2019 none of which tested positive.
Secondly if they were false positives, I would expect them to be randomly distributed. Not concentrated in the affluent capital city, and not solely in the second cohort with none in the early march cohort (as you would predict if exponential growth is occurring).
Your second two points are fairly compelling.