Blender 2.64 official.
Attached image and blend file. Objects in center don't have applied modifier.
Yellow selected vertices are selected with Menu > Selecy > Non Manifold operator. It usually happens on sharp corners with smooth and sharp modes.
I usually dealt with it using Non Manifold select + Collapse Edges
Green circle shows small cavity, appears with sharp mode.
If I may suggest. If creating triangles will fix those problems, it would be ok. Triangles are not problem with so much dense and uniform meshes.
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Confirmed the bug. Quick test with Polymender shows that this might not be a problem with the underlying algorithm, but rather a bug in Blender's modified version of it. Will investigate further.
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A better description of what's going on:
Attached a simpler test file as remesh-bug-01.blend.
To see the bug: apply the modifier, enter edit mode, and select non-manifold with ctrl+shift+alt+m. Observe that two edges are selected where the surface pinches together.
For comparison, the original Polymender binary produces a mesh that appears identical, but has separate vertices and edges in the pinched areas, thus producing a manifold result. To test this, get the Polymender rar from http://www.cse.wustl.edu/~taoju/code/polymender.htm (works with Wine if you're not under Windows.)
Export the mesh without the modifier as a .ply, then run "PolyMender-qd.exe remesh_bug_01.ply 3 0.99 output.ply".
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Some further investigation:
Enabling the use_manifold option within the dual contouring octree does fix this issue (and gives identical results to Polymender.) It introduces new problems however, because it duplicates both vertices on the edge, not just the interior vertex. This means that faces of five or more vertices are generated, with one or more edges of zero length. It's not clear to me that this configuration is really better.
In some specific cases I tested, it is possible to modify the manifold_table array to only duplicate one vertex and produce nice quads around it. The manifold_table has 256 cases in it though, and I am not at all confident that such fixes wouldn't introduce new bugs for other inputs. I think it's best to leave this behavior as-is.