Copying Visio 2007 drawings and embedding them into other documents can have startling effects. Lines can get routed differently, breaking a careful layout. Dotted lines can appear as solid lines, making it confusing to distringuish between different types of objects. There are 2 important things to know that can help avoid these issues.
Using Copy Drawing (Visio) and Paste (Word) results in a correctly formatted embedded Visio document
[HKEY_CURRENT_USER\Software\Microsoft\Office\12.0\Visio\Application] "MetafileDashLineAsSolid"=dword:00000000
Even better news: This process is no longer necessary in Visio 2010. Drawings are reproduced correctly when pasted into a Word document, even when only a subset of the objects is selected in Visio.
THANK YOU SOOOO MUCH!!! I have been looking for hours for a solution to my problem (copying from Visio into Work without losing the dashed lines – they transformed to solid lines during the copy/paste function). A very helpful and easy fix to a frustrating problem.