I'm writing a paper where I have a number of sentences across a few paragraphs, all from the same source. How should I use inline citations in this situation? Should I put them after each listed fact in the sentence at the end of each paragraph, or at the end of all of the paragraphs? The paragraphs are all topically related, but each one is different enough to be a sub-topic. In case it's relevant, the topic being discussed is technology, the paragraphs detail how companies using that technology.
From what I've seen, the only situation in which you would use a single citation following multiple sentences is if it's obvious that you're quoting that source verbatim AND the quote is uninterrupted. If you're using your own terminology OR the quote is interrupted, you should cite each sentence separately.
This becomes obvious when considering the purpose of a citation. Citations are there to answer the question, "who said this?" If you're quoting someone verbatim, and it's obvious you're doing so, then you only need a single citation, as the reader will infer that it applies to the entire preceding quote.
On the other hand, if you have multiple claims throughout a paragraph, after each claim the reader will wonder, "what's his source for this?" In most cases, you will be using multiple sources, and you will have a mixture of references. However, even if you have a single source for lots of claims, the reader will still wonder after each claim what the source is. You should tell them the source of each and every claim separately.
The exception I've seen—and that my advisor requested I use in my writing—is in the instance of a single logical thought pattern being followed throughout a paragraph or set of paragraphs. If you're describing someone else's work, it can be justifiable to state, "the following is an overview of Bob (2007)", or something to that effect. From my experience, though, that usually only happens in review articles.
If you really have only one reference which you take one paragraph to sum up, I'd really advise eykanal’s last item (the “exception”):
Tying one’s shoelaces with only one hand is notoriously difficult . Although it seemed like an unsurmountable issue a few years back, the recent breakthrough of Smith et al.  relied on a few topological considerations which have been clearly delineated by Brown , and are summarized in the rest of this paragraph. [Here your description, with claims from Brown, without repeating the reference number]
However, little is known about the influence of the number of fingers used  in the tying process. Here, we present a research on tying shoelaces with even-fingered hands.
This is better than having a lot of claims  with the same reference  written all over one paragraph . However, you need to make it crystal-clear what part is covered by the reference: using the paragraph boundary (and explicitly stating this) is a good way of doing that.