Mary-Claire van Leunen's Handbook for Scholars argues against bibliographic footnotes (which saves space, makes a "handsomer" page, and avoids interrupting the reader's attention – all of these are "automatic benefits").
The main change is to embed the citation. But embedding is not a mechanical process.
Knuth embeds citations entirely in The Art of Computer Programming which tends to be frustrating (since he uses the old fashioned approach using abbreviations harder to crack than the Purple Code). Just remember that the volume is always in bold...
The basic elements to a bibliography item amounts to three things
3. Bibliographic Information.
There are also two optional extra data that could be provided:
4. More bibliographic information;
The bibliographic data in (3) describes the work you have before you that you are quoting and referring to. The bibliographic data in (4) describes some other version of the work that you know about and that your reader may find more accessible than your version.
So, for example, consider this paper on the arXiv. How to format it in the bibliographic format appropriate? Well, it would be:
|Author||→||John C. Baez, James Dolan.|
|Title||→||"From Finite Sets to Feynman Diagrams."|
|Bibliographic Information I||→||In Björn Engquist and Wilfried Schmid, editors, Mathematics Unlimited – 2001 and Beyond 1, pages 29–50, Springer 2001.||Bibliographic Information II||→||arXiv:math/0004133v1 [math.QA]|
Regarding the extra bibliographic information, van Leunen advises:
Are you referring to a rare work? Your inexperienced reader will want to know how to get hold of another copy. Are you referring to an expensive hardcover? Your impoverished reader will bless you for mentioning the cheap paperback as well. Are you referring to a pirated Taiwan edition? Your reader of tender conscience will appreciate knowing about a version on the up-and-up.
Random House (1978) page 174
Now what's with the last bit of information? Well, it's annotations that may be useful. Is the book factually incorrect but has useful diagrams to refer to? Is the author of the eprint a crackpot? What should we know? Why are we using the reference anyway?
Personally, the rule of thumb I try to abide by is: throw all the details you can about the reference you are using. Don't use ambiguous and cryptic abbreviations. And, in my own notes, when I refer to a library book...I also tend to put the call number down (and the library I got it from).