\dotfill is defined via \cleaders and an infinite glue specification (\hfill). A similar definition of \vdotfill has two problems:
\leaders and friends only work with horizontal glues in horizontal mode or
vertical glue in vertical mode. Orthogonal variants are not available.
There are two vertical directions (height and depth) instead of one horizontal. That raises lots of new questions: Where does the fill start? How are direction(s) and and amount(s) specified?
PDF operators
If the TeX rule is implemented by a line in the PDF page description, then
the graphics state could be changed to get a dashed line, may be with rounded line ends. However, a rule can also be implemented by a filled rectangle, where this trick does not work.
Clumsy workaround for pdfTeX
The vertical positions via \pdfsavepos (the module zref-savepos of project zref provides an interface) can be added in pdfTeX at the base line and via \vadjust (after) and \vadjust pre (before the current line). The latter is a specialty of pdfTeX. The the depth and height can be calculated and the vertical dotted line can be set.
However, this will not work in all circumstances. For example, other material might be added via \vadjust interfering with the position measurement.
Solution sketch with LuaTeX
LuaTeX provides a new feature "attribute". Thus, a normal \vrule with the correct width can be set with an attribute meaning a vertical dotted line.
Then the built page (its node tree) is traversed to find such rules to replace them with dotted vertical lines.
\vrulehas the ability of adapting itself to the height and depth of the enclosing box. – egreg Jul 29 '15 at 19:40\vdotfillto automatically adapt to the surrounding height and depth? – Gonzalo Medina Jul 29 '15 at 19:42\valign. ;-) – egreg Jul 29 '15 at 19:47