NavList:

Tony, you wrote:
"Will a sight of a star near zenith taken with a bubble type sextant be more reliable than a sight of a star at medium/lower altitude taken with a Newtonian type sextant (referenced to the natural horizon)?"

Newtonian type sextant? Hmm... Have you encountered that name in print? I would not refer to any sextant that way despite the claim that Isaac Newton originally invented the instrument. It would be more natural and probably better for communication to call it a "reflecting sextant" or a "marine sextant" or even just a "common sextant".

My short answer to your question would be: normally no, but under rare circumstances, yes. However the qualification of "near the zenith" is un-necessary. If an instrument is accurate at 80°, then it's accurate at 45°. There are circumstances, however, especially for some navigators who "do it wrong" where a marine sextant becomes quite inaccurate at high altitudes. The simplest case where a bubble sextant beats a marine sextant is when the horizon is obscured completely. If there's surface fog, you can often see the Sun up high and could take sights with a bubble sextant.

You suggested it might be more accurate because of... 
  "more precise sextant positioning in vertical plane". 

Have you tried bubble sextants? They're pretty tough to position in the vertical plane! And what difficulty is there getting a marine sextant in the vertical plane? Yes, many navigators learn to swing the arc wrong at high altitudes. But that gets fixed by better education, right?

And you suggested
  "less or negligible refraction correction required".

But the refraction correction is easy and reliable. Note that this is separate from the refraction portion of dip, refraction of the horizon (which you bring up next). There's no problem using a marine sextant or a bubble sextant at almost any altitude, and the refraction tables (with corrections for temperature and pressure below 15° altitude or so, if necessary) accurately correct for the astronomical refraction. No problem.

You also wrote:
"Been to Finnish Gulf this weekend, compared the height of a distant island/fort - in the quiet air and sunny conditions the refraction was very diffrerent to our usual conditions - I could measure the refraction to alter the height of the island as much as by 4' (four arc-minutes) in unfavourable weather. This time the fort at ~5km was in full view and the next one - in ~10km was clearly visible too."

See, that's a distinct issue from the refraction of the altitudes of celestial bodies. This is anomalous refraction of the horizon --a modification to the dip. It's fascinating stuff! And yes, this is the big limiting factor on the accuracy of traditional sextant sights when the horizon is used as the reference, as it is with a normal marine sextant. Even under good circumstances, it can amount to half a minute of arc. In unusual conditions, it can amount to 5 or even 10 or 20 or more minutes of arc. Anomalous dip can be a big problem with enclosed bodies of water when there are temperature inversions and other oddities in the structure of the low-lying layers of the atmosphere. There are no tables for this -- no equations that will "un-do" the anomalous behavior, despite 150 years of experimentation and ideas. So in a case of extreme anomalous refraction, or in a case where the sea horizon is lost to refraction or just plain-old fog, a bubble sextant wins. Fortunately, on the open ocean, anomalous refraction is greatly reduced under most circumstances. Exceptions are found where there are interesting temperature phenomena, like in the vicinity of the Gulf Stream and in the Red Sea and any similar areas.

Frank Reed