Our old friend "duplicate content" comes back to haunt us.
Yes, if you have two different URLs pointing to the same page – even though you've only got the one page on your server – Google can think they are two different pages and so index them separately, splitting the link juice between the two.
The easiest way round this is the "canonical" tag. Choose the format of the URL that you would prefer Google to use and then put it in the <head> of the page, like this:
<link rel="canonical" href="http://www.example.com/">
Whenever Google finds that bit of code at a page that it thinks has a different URL, it then knows that the URL it has found is just an alias for www.example.com/ and so considers them to be the same page.
The one thing to be really careful about is that if you create new pages by taking existing ones, stripping out the text and using it as a template, you must make sure that you change the canonical line for each different page, otherwise the home page will be the only one that Google ever indexes!