What factors should an inventor consider when deciding whether or not to include references to other art in the background section of their patent application?
It no longer seems to be a common practice.
The factors to be considered are (1) setting a background or context for the state of the art in the field of the invention and setting up the problem which the invention solves, and (2) giving the examiner admitted prior art.
While a thorough description of the prior art may be good on a scientific level (showing that the inventor really understands the field and the problems in it), in patent prosecution (i.e., getting one) and litigation (i.e., enforcing one) it's dangerous.
If an application meets the statutory subject matter requirements for a patent and it is not identically disclosed elsewhere (35 USC 101 & 102), it will still frequently be rejected as obvious over a combination of references in the prior art (35 USC 103).
The applicants, if they don't agree, can then try argue (among other things) that one or more of the references do not, in fact, constitute prior art. For example, in an application in the art of baking, if the examiner found a reference disclosing a critical step, but the reference was in the field of nuclear physics, the applicants could argue that nuclear physics is unrelated to baking, and an ordinary baker would have no knowledge of art in nuclear physics. However, if you state in the application that something is prior art, then it is - and it's practically impossible to undo it later.
So, the practice of citation of specific prior art in the Background section of the application is becoming less common because there is no real benefit to it for the purposes of either getting a patent or enforcing one, and there are potentially serious negative consequences.
In Australia, the test of prior art includes common general knowledge and one or more pieces of prior art. We can't normally combine pieces of prior art unless it is logical to do so - referred to as incorrect mosaicing. However, if a patent mentions prior art, then it would be logical to read the documents as one document. Therefore all the pieces of prior art can be combined to use them in an invalidity claim.
Thus, citing prior art is a very bad idea.