As for the Scottish Independence Referendum (Indyref) - the three main points which were pushed by the Better Together campaign were;
- A NO vote to remain in the UK would see a 'DevoMax' situation where many more legislative and governmental power would be devolved to the Scottish Parliment and taken out of Westminster's hands
- An independent Scotland would not be able to use the pound
- The only way to secure your place in the EU was to vote NO and remain in the UK
These issues had a huge effect on the Indyref as they, especially the last two, carried a reasonable doubt to anybody with the capability to think rationally. We can see how since yesterday the pound does not seem so solid anymore and in fact the day after the NO result the backtracking began on all of our shiny new powers at Holyrood.
Most obvious and concrete, though is the fact that voting to remain in the UK did not in fact preserve my or any other Scot's place in the EU. We are being led out after an unquantifiable but assuredly notable percentage of voters in the Indyref voted NO to remain in the UK and in the EU. Now that seemingly solid guarantee has been reversed it is reasonable to assume that a large number of voters (remember that the NO vote won by a 5% margain - only a 2.5% swing) are now reconsidering their vote and would vote YES to an Independent Scotland in order to remain an EU citizen.
You could also add that people may have changed their mind due to the backpedalling on 'The Vow' as our promised new powers were collectively labelled and because of the uncertainty of the pound's future. There are many other points to consider, but this overall majority of Scots who wished to remain in the EU should and must not be ignored and while I agree with @JuveJay to an extent that talking of a second independence referendum is opportunistic in a way it is also a conversation well worth having considering how much the fundamental arguments which drove the result in 2014 to a NO vote have changed. It may be opportunistic but to ignore the change which has occurred would be neglegent, particularly for an elected head of Government whose heavily pro-independence party won a staggeringly convincing victory across Scotland in the most recent elections, to ignore.
A second Scottish ref would be a disaster, a large amount of people would vote out of spite more than anything else.
Scotland has got and will continue to get more powers, we have already done fantastically well in completely over taxing us for property purchases. The pound will be fine, it was always going to head down after the result, once the uncertainty eases the stability will return.
I find it ridiculous that people calling for independence on the back of this result, given the fact that it would be a very similar move to us coming out of Europe.
There are still huge (even bigger than before) issues in Scottish Independence:
1. We do not have a currency. We cannot "just use the pound" as we would not be able to control our monetary policy (one of the key issues in controlling an economy.
2. The oil price has crumbled, SNP predicted oil at $110 to make a barely credible argument in the last referendum. Oil is now $45.
3. Would we even qualify to join the EU? I'm not convinced we would meet the targets and it certainly wouldn't be instant.