I used to play 12 string on most any song I did with acoustic, and used a capo as well when needed no particular problems.  I think it's just what you're used to playing, if one mostly plays 6 string & electrics then a 12 string is going to be challenging.  These days I usually just use my JTV 59 Variax.

Dan

You might find you'll be better off recording the song in sections, moving the position of the capo as you move between different sections.

I use a G7th capo. The trick is to fit it carefully by pressing the bar down straight on to the strings, without moving sideways or otherwise disturbing the strings, before clamping.

The other trick is to have a reasonably low action and have it properly in tune first 

Are you using a "quick" capo or the kind that wraps entirely around the neck with the screw clamp? I find quick capos can sometimes not apply enough pressure evenly on all the strings... even on a six string guitar. Might be something to consider. And yeah I'd look around to see if you can find a capo specifically designed for 12 string. Also spend a little more on a quality capo. It may seem silly for such a simple device but in the studio you want accuracy. It'll save you more time doing takes and trying to brighten deadened tones. Cheers.

Oh and although I've only worked with capos when absolutely forced to by anal band members I've been told more than once that tuning AFTER the capo is in place is a no no. With a proper capo on a guitar that has good intonation you should be able to tune up the guitar then apply the capo. If it is out of tune at that point something is wrong. The three likely culprits are 1) the guitar wasn't actually tuned properly 2) the guitar has an intonation problem or 3) the capo was put on crooked or improperly and it's bending the strings (sometimes even if it goes on straight if you have "tall" frets the pressure from the capo can knock things out of whack which is another reason why the screw down capos are better). If you tune with the capo on you are creating a situation where the string tension may not be distributed evenly on each string (there could be more or less tension above the capo) so when you start playing that tension gets released below the capo and you go out of tune. Cheers.

There are a couple of companies that make capos specifically for 12 strings. I've always had good results with Shubb capos on guitars and Dobros.

You can check 'em out here, if you're interested: http://www.shubb.com/

Taylor 754... Recording one with it now. But this sweet piece of wood and steel stays in tune ;-) Drop a few large on an instrument and they're typically better made.