I’ll admit it. I am a librarian and I hate footnotes and endnotes.
I have often lamented the wide proliferation of citation styles. I really wish publishers could all agree on one style of citation, but that probably won’t be happening anytime soon.
This afternoon I am trying to read an article that seems very interesting, but it has endnotes, making my preferred style of reading a journal article much more difficult.
For example, normally I start to read the first few paragraphs of the introduction, then skip to the references section to see who they are citing. A nice neat alphabetical list makes this easy.
Footnotes, on the other hand, make it very difficult to scan the references cited.
Today, when I wanted to check on a particular reference, I turned to the end of the paper and found endnote #90 and read “Ibid”. I kept looking up the list to see “Ibid. Ibid. Ibid.” until eventually I found an author and article title at endnote #85. But then I have to keep going back up the list (of over 100 endnotes) until I saw a complete citation. In this case, I didn’t find it because it was buried in one of several paragraph long notes (note #76). I had to turn to the “search” feature of my PDF reader to actually find the complete citation.
This is not user friendly. I argue that a nice list of alphabetical references and author date in-text citations are the most user friendly (although my colleagues in the humanities may disagree with me vehemently).
I grant that footnotes or endnotes can occasionally be very useful for text explanations, but most of this explanation could often be done within the text. And of course, there are authors who use footnotes to humorous effect (Jasper Fforde being one of my favorites).
OK, rant over.
the Undergraduate Science Librarian 
You grief seems to be with the tracking references, rather than footnotes per se. I prefer the referencing approach used in the sciences, myself, but then I’m accustomed to it.
Leaving aside humorous use, IMHO footnotes should really be for things that would disrupt the flow of text. I use them, for example, in science blogging if I want to make a technical aside that would be disruptive, confusing or a distraction to a casual reader.
Grant, You are exactly right. I agree that footnotes can be used effectively for the types of things you describe. They can also be abused in that way too – I think writers always need to think very carefully about whether something absolutely has to go in footnotes, because footnotes can be distracting to those who want that additional information.
I hate it when a combination of rushed writing and editing on-the-fly makes me look silly. That first sentence ought to start:
Your grief seems to be with tracking the references…
Sigh
Anyway, I agree. It’s a lot about how you choose to use the tools, as it were, rather than the tools themselves.
In the example I gave I am trying to cater for more than one type of reader. In the case of the more motivated reader, I’m working on the basis that their extra interest will mean they’re happy to track down to the footnotes. I’m leaning in favour of the more casual reader in order not to put them off.
You might also want to read the article I’ve linked on my name in this comment. In it I point out that a related issue (links) can be viewed as technical issue, rather than a writing one. (Skim over the first few paragraphs.) You could say the same for footnotes. There is no real reason that they have to be implemented in the same way as print on the ‘web.