First, make sure you are using the same version in both places.
Second, margins are a concern (Ryk has a good point, even though I've never personally noticed the issue), try not to mess with them to the point that your image is 0,05" from the border of the page. Keep some margin (pun intended) for error.
Third, never, ever align text by using additional space or enter strokes. Use tabulations (learn how to set custom ones, it'll be handy), increased line spacing, spacing before and after paragraphs, and forced page breaks.
Fourth, as Art_Jeffries said, use standard fonts if you're going to carry a document from place A to place B (or make sure both places use the same font and this is even more important if you are bringing a Powerpoint presentation with you... unless you like giving a presentation in Wingdings).

As for graphics moving, make sure you use the setting that keeps it aligned with the text, and then, *respect its limitations*. Yes, that means keeping the graphic within the margins, and it may mean that the graphic needs to move somewhere farther away from the text it concerns.

So basically, good habits will hold you in good stead and prevent a host of problems.