I\'m using Mac OS X Lion, Terminal.app and Tmux version 1.6. I get a dashed line as a window border instead of a continuous line that I get when I ssh into a Debian virtual mach
Actually, some fonts you like only contain a small number of glyphs to display usual characters, but failed to include glyphs for other unicode characters, for example U+2502, which is used by tmux as the vertical split line. So the system usually defaults to a fallback font, however, unfortunately, that fallback font does not provide the glyphs that are appropriate for drawing a continuous line.
One possible solution is to use terminals that supports selecting a fallback font, such as iTerm2, then you choose Menlo as you mentioned as the non-ascii font and use the original font as the same time.
The other solution requires a little more work, use fontforge or other font editors to patch the missing glyphs using those from a correctly displayed font like Menlo. Here is a link to what I have done, patching Inconsolata for Powerline using glyphs from Menlo: https://github.com/Determinant/inconsolata_for_powerline_mod