Possibly because Denmark has been an independent country since times immemorial, the country doesn't have a national day, so Constitution Day is the closest you get. It's not a day of big celebrations, though -- in general, people gather to listen to politicians speaking about the value of democracy, but that's about it.
However, I do like the fact that the country has chosen to celebrate its constitution, rather than some battle or royal event. I guess the Scottish Constitution will come into force on the day Scotland becomes independent (March 2016?), so constitution and independence might become interwoven for Scotland, too.
When Scotland becomes independent, it would be a wasted opportunity if the new (or rather, reborn) country didn't get a written constitution -- the UK's unwritten one has always struck me as a bizarre contraption.
Without going into the details of what it should and shouldn't say, I have a few ideas about the length and scope:
It shouldn't be too long. If it is (like for instance the doomed Constitution for Europe), it will be too specific, which means that it will need revising all the time, and by doing so, it loses its constitutional nature.
It shouldn't be too specific. Apart from the problem with continuous revisions if it is, it also creates problems if external factors require a constitutional change that there might not be a political will to implement.
It shouldn't be too hard to change. If it is, it will start to be reinterpreted, with the result that nobody really understands what it means. For instance, the Danish Constitution is almost impossible to change (it was last changed in 1953), and when it mentions the king, it means either the queen, the prime minister or the government, depending on the context, which isn't ideal.
It should be easy to understand. Although many laws are by nature highly complex, the constitution should be a straightforward text that school children could learn and discuss at school.
It should make us proud. Like the Declaration of Arbroath and other such documents through the ages, a good constitution should be an inspiring document that will inspire its readers centuries for now.
If all of this seems a bit daunting, at least there are plenty of existing constitutional documents from all over the world than can be used as a basis, so it should be doable.