gassor
There may be more posts after this.
Eire and the UK are in a common passport area. This area is also part of the EU, although separate to the bigger Schengen area.
NeuScotland would have to negotiate being allowed to continue as part of that area.
Not being in the EU (as seems likely for Scotland) and having a very different immigration policy to the common area (as stated could be the case by Salmond - Scotland has a bigger need of young skilled workers than the UK as a whole) may make that a problem as well. You can't really operate different immigration policies in a common passport area.
Eire and the current UK are in the EU together (free movement etc) and have substantially similar immigration policies - deliberately to facilitate this. All visa agreements with other nations are the same etc.
http://en.wikipedia.org/wiki/Common_Travel_Area
If Scotland wishes to apply for EU membership, it would have to agree to joining the Schengen Area (current EU policy for new members) after the minimum qualifying period, demonstration of fiscal propriety etc - along with the Euro, or somehow get an opt out agreed in a process where any member state could easily veto exceptional requests.
http://en.wikipedia.org/wiki/Schengen_Area
Good answer, thanks.