NavList:

My apologies Bill for misquoting you.  I meant no harm.  That's my memory modifying your statement.

As to reading the vernier and deciding which is the appropriate reading, I like to do the following.
1) There is a modest parallax between the vernier lines and the arc lines.  It is therefore important to view the final alignment when those lines are centered in the field of view of the microscope.  That microscope is on an additional axis of rotation on the index arm, permitting centered view.  I take advantage of that.  If you don't, its easy to be off by 10 or (in terrible cases as you point out) 20".
2) Once I decide which pair is best aligned, I center the FOV over the pairs on either side of the central pair.  The vernier lines for these pairs should appear slightly offset towards the center pair (on my Heath).  This is an important criteria for making the final call.
3) Since the vernier reading is an offset to the nonius reading, I like to record each individually and do the quick sum on paper.  Its easy to make an arithmetic error when doing this in your head.  {Note: the same applies when doing the autocollimator reading.  The AC has independent minutes and seconds, with independent signs.  +1' -30" is the same as 0' +30" although the presentation is different at the graticule}

That said, reading a vernier takes practice and care.  The resultant minor loss in accuracy due to lost motion and imperfect worm gears (by your measurements) is outweighed for many by the ease of reading the micrometer.  Its a tradeoff that history has decided for us.

There is one artifact that has troubled me for some time.  Nearly all of the non-electronic means of sight reduction for LOP based navigation is based upon tenths of a minute (6").  Yet the vernier sextant yields 10".  This mismatch, when doing reductions, forces a round off to the detriment of the vernier reading.

Consider
10" ~ 0'.2
20" ~ 0'.3
30" = 0'.5
40" ~ 0'.7
50" ~ 0'.8
60" = 1'.0

What happened to .1, .4, .6 and .9?  They don't line up to the modern tables. 

I believe these vernier instruments more appropriately align to the Latitude at Noon // Time Sight in the AM PM method, and the micrometer sextants align more appropriately to the LOP era.  I wish to treat this as a supposition and not a statement of fact to be trolled.

Brad