If I build a page with different paragaprhs taken from different sources will that page be counted as duplicate content or unique by the SE?
That is a great question! But I always look at the search engines as if I was looking at a page. If I saw that i would say yup duped content, so imo so would the engines.
It will not be counted a duplicate content as long as you get more link power than the other sources....Duplicate content only exists if you have less link power...this is why Google suggests to link back to the original source that way the original source usually will have more link power....
Being indexed and ranking highest are two completely different things. As for the original question, the document will be unique.
Does this mean that I could include a large portion of public domain material in the middle of a page, and it won't be seen as duplicate content by se's?
Well yes and no. The document as a whole will be unique, and a query for a phrase contained partially in your text and in the public domain text will pull you up higher on the search. However a search of keywords contained only in the public domain text will "most likely" see them rank higher depending on what you added to the page does to you keyword density. For example: A search for "My Text" and you will rank, a search for "Public Domain" and it will rank however a search for "Public Domain Text" you will rank because the public domain doesn't have a great match for all the like you do. This is all being equal such as links to both documents, Title tags etc right down to the smaller things like code to content ratio of both pages. Hope that makes sense.
Its duplicate content and it will be noticed by search engines. Thats why the crappy Lycos Retreiver is a failure - its banished into supplemental results because its all scraped content.