However, if they are not EU members and find themselves even temporarily outside the EEA (the European Economic Area that consists of the EU and EFTA countries) then that could effectively stop the free movement of people, goods and capital. It's possible that people from Scotland would need a visa to enter the UK unless a bilateral agreement could be make (such as the UK/Ireland agreement that exists outside the EU). This has the potential for being absolutely catastrophic.
The currency is also difficult, it has been argued that the Scots could have a once-side currency union with the pound sterling even if the UK did not agree. This sort of system already exists in the Isle of Man and Channel Islands, but those are not independent states as such (but nore are they part of the UK). However, there are only a quarter of a million people on those islands and Scotland has more than 20 times the population and 25 times the GDP, so it's a different league altogether.
But the clincher for me would be the sheer amount of paperwork involved if I were Scots. Am I Scottish or English or what? What about my family members? Where will my bank account be? My pension? My job? How do I get across the border? Even if everything goes smoothly, there is an immense amount of effort needed from citizens of the UK to straighten out all these details.