My visa was denied ;(

This is a good guide about self employment, from the CAB (Citizens Advice Bureau) for Scotland.
http://www.adviceguide.org.uk/scotland/work_s/work_self_employed_or_looking_for_work_s/self-employment_checklist.htm

Have a look and see what he has or hasn't done (why hasn't his accountant sorted all that?). Then get the documents from him that you will need for your visa. As ksand said, getting your visa is about ticking boxes.

Don't get upset about this. It will be something to tell your grandchildren.

Having a read through, it looks like the issue is the shortfall in documentation.  When you're talking about a visa refusal, lack of documentation is probably the best reason why you could get refused.  (even though I'm sure it doesn't feel like it at the moment)  If there was something more fundamentally wrong with the application - like he didn't meet the financial requirement in the first place - that would be something not easily corrected with a fresh application.  But in this case, it looks like the missing documents is what caught you out, and that can be addressed relatively simply.

These visas are checklist ones, to borrow the term from ksand again.    If you can check off everything they ask for, you'll be fine.  It looks like they've given you a list of exactly what they need from the appendix, and if you can sort out the paperwork and address every point on that letter, I think you'll be fine with a new application.  I would recommend though that if his book-keeping does need serious sorting, you might want to get more professional help with that to make sure he's doing everything he needs to do being self employed - and that he has (or can get) all the paperwork you need.

Hope we've been able to help a little, and don't fret too much.  Your second application I'm sure will be fine!   

Flying into Glasgow and going on to Denmark should not be a problem because you won't have to clear Immigration until you get to Denmark, I believe.

Can anyone verify for sure?

Having been held up in Edinburgh before, I can say firsthand how awful an experience it is.  Even with my return ticket to the US, they were merciless and kept me in a room for over 3 hours before a decision was made to let me enter the country.  In that time I was stripped of all my personal belongings, including all jewelry, and made to just sit in the room.  I was never offered water or tea or even a tissue (because I as bawling my eyes out.)  They did not notify my fiancé (now my husband) until over 2 hours in and we had people there waiting to greet me as well.  Degrading and embarrassing.

Flying into Glasgow and going on to Denmark should not be a problem because you won't have to clear Immigration until you get to Denmark, I believe.

Can anyone verify for sure?

I would definitely NOT risk it.

The only way you won't clear UK immigration is if you have a scheduled connecting flight out of the UK with the same airline, as part of your ticket from the US, where your luggage is checked all the way through to Denmark. And even then, you would still need to apply for a Direct Airside Transit Visa (DATV) before you can fly through the UK.

If you have booked the two flights separately and will have to collect your luggage in the UK and re-check it onto the second flight to Denmark, you WILL clear UK immigration and will need to apply for a Visitor In Transit visa before getting on your flight in the US.

The LAST thing you should be doing right after a visa refusal is attempting to travel into or transit through the UK without a visa.

If you absolutely must see each other before trying to apply for the fiance visa again, then either he should travel to the US to visit you, or you can meet up in a third country, whereby you do not go anywhere near the UK in transit.

You got a good deal by purchasing the return ticket instead of a one-way back to the US, so if you don't use it on Tuesday, then it's not like you've wasted your money and you're not losing out on anything. Just think of it as making a saving on what would have been an expensive one-way flight back home to the US.

if i purchase a ticket out of the uk airport for a few hours later to a different country in Europe (I have close family in Denmark)  and also explain that I didnt want to lose money for the ticket I had purchased.... will they let me fly from Scotland to Denmark with absolutely NO stepping foot out of the airport??

Is your family in Denmark Danish? If so, are they closely enough related that you may be eligible for Danish citizenship? If you are, it might take awhile to get Danish citizenship (I don't know anything about Danish citizenship laws/process), but you wouldn't need to have any visas at all to live in the UK.

Oh, honey.  I am so sorry for you.  Worried to death about my own visa app (which I'm not even doing until 2016,) and I know you must feel devastated.

I'd recommend him getting a lawyer/solicitor, to help him sort out his missing financial docs. 

Or, perhaps reapply using savings to meet the financial requirement?  If he has enough in savings, that might be an option.  It's a huge amount, though.

Seconding the Danish citizenship idea!  Any way at all that'd be possible for you? 

I don't think I'd risk travelling.  You don't want any blemishes on record to mess up your reapplication. 

Take a deep breath, have a good cry if you want, and try to stay clear-headed about the whole thing.  I can't offer any real advice, but I do offer my empathy, truly.

Having been held up in Edinburgh before, I can say firsthand how awful an experience it is.  Even with my return ticket to the US, they were merciless and kept me in a room for over 3 hours before a decision was made to let me enter the country.  In that time I was stripped of all my personal belongings, including all jewelry, and made to just sit in the room.  I was never offered water or tea or even a tissue (because I as bawling my eyes out.)  They did not notify my fiancé (now my husband) until over 2 hours in and we had people there waiting to greet me as well.  Degrading and embarrassing.

Good grief, that was just down right cruel! 

What an awful experience you had, and I'm so sorry you had it.  I though my little delay in Heathrow last year was stressful and embarrassing (and it was, as I was completely unprepared for it having traveled to the UK in the past), but it was nothing compared to that. 

Meredith, I don't have any advice for you (you are getting great advice from the wonderful and knowledgeable people here at UKY in any case), but I do want to send warm hugs and hopes that this experience will soon be in your past and you will be with your fiance to start your new life together very, very soon.