This is more a question about Stata than it is about LaTeX. You use Stata to generate the graph and pdfLaTeX does not change it. If you open the graph in a viewer that is capable of displaying EPS files (e.g. Ghostview) you will find that the missing edges are already in the EPS.
In Stata there is not much you can do about it, except for explicitly choosing a different marker symbol with the
msymbol option, e.g.
scatter mpg weight if foreign, msymbol(O)
graph export filename, as(eps) preview(off) replace
help symbolstyle and
help scatter##marker_options in Stata for more information about marker symbols.
From what I saw, the triangle, square and diamond marker symbols all have a missing edge as do bars/boxes on bar charts, box plots, histograms.
If you are not familiar with Ghostview: Ghostview is a command-line only programme, but you can use GSView for instance as a GUI on Windows. Some programs like SumatraPDF can also display EPS files, but they also use Ghostview as a backend AFAIK.
It is sometimes helpful to also post on which platform (Windows, I presume) and with which software versions (Stata 11, 12?, Word, Acrobat/PDFMaker) and tex distributions (MiKTeX 2.9?) you are working. In this case it does not make much of a difference, I guess, except that Stata 12 on Windows is now capable of exporting PDF directly (on Mac you could do that at least with v11 already and on Linux I don't know). When exporting to PDF with Stata 12 on Windows, the diamonds are missing an edge as well, but strangely the squares don't (while they do when exporting to EPS - at least that's what I saw when testing it ad hoc).
It could be worthwhile to post this as a bug to Stata Corp. by the way.