From where I am sitting in Brussels, the interesting thing is the consequence for the relationship between Scotland, the remnant UK of England Wales and Norn Iron, and the EU. The only serious study of this that I am aware of (discounting any statement from any politician anywhere, of course) is a House of Commons research paper which comes to the sensible conclusion that nobody really knows what the consequences of Scottish secession would be vis-a-vis Brussels. If I had to bet, I would expect that the least difficult option, of treating both Scotland and the remnant UK (rUK) as inheriting the current UK membership, keeping all the British opt-outs as long as they want to, is the most likely. There will be objections from the likes of Spain, worried about the demonstration effect, but in the end if a sovereign state becomes two sovereign states by legal means, it's not really anyone else's business.
An independent Scotland would have the same number of seats in the European Parliament as Ireland, Finland, and (soon) Croatia, currently 12. The rUK might well get away with keeping 72 seats, ie more for England and perhaps Wales (not Norn Iron which is already over-represented), as its population shifts from just ahead of Italy to just behind. All the EU acquis is already Scottish law. I can't see any formal problem.
Where I can see a problem, as hinted at in this AFP article quoting anonymous EU sources, is that the necessary renegotiation of the rUK's relationship with the EU following Scottish independence will necessarily be so huge that it must trigger the 2011 European Union Act requiring a referendum on any significant Treaty change - and if it doesn't formally do so, the political pressure to have a referendum on the new terms of rUK's EU membership will surely be overwhelming. And unlike the outcome of the Scottish independence referendum, the outcome of any UK or rUK referendum with the word "Europe" in is far too obvious. In my view, one of the unexpected by-products of Scottish independence may well be that the rest of the UK leaves the EU entirely.