WordPress SEO by Yoast causes a conflict with WP-Invoice and from reading some of the other conflicts, I believe it is a coding error/bug with WordPress SEO.
From Anton Korotkoff of WP-Invoice:
It is the same conflict with Simple Facebook Connect as with WordPress SEO by Yoast.
I remember you are not a developer by I'll try to explain what happens there:
There are predefined (standard) hooks and filters inside WordPress.
Hook is a place in code which we (developers) can use to do some things in specific moments.
Filters are similar to hooks but are used to filter data when it goes through functions.
So, there is a filter named 'the_content' which we use to show invoice content (information + payment form). This filter is standard wordpress filter and called by wordpress only once (Should be called once) when showing page. But some plugins such as 'Simple Facebook Connect' or obviously 'WordPress SEO by Yoast' call that filter somewhere in code too. But they mustn't. Such behaviour causes applying our filter for every time they call 'the_content' manually. That's why you see two or there invoice copies on a page in different places.
Hope this is clear...
I'm personally trying to find a way to fix that because I understand that authors of that plugins even didn't hear about the conflicts they created somehow since everyone blames those who are less popular.