Be prepared to handle deadlines and contingencies that come
with offers.
For example, if you get an offer with a two week deadline (not uncommon)
be prepared to contact other prospective employers to let them know.
Thus it would be good to have your order list in mind before an offer comes
through. Also be prepared to ask about terms of the offer and what is
and is not negotiable.
Once you sign on the dotted line it will
be much harder to ask for changes to your offer.
Another example for fresh PhDs is that many postdoc positions are offered
contingent upon the candidate completing the degree.
Occasionally students do not finish on time and even more occasionally they
do not realize that they can not complete their PhD while in their new position.
If you discover, after accepting a position, that you are not going to
graduate on time, it is best to contact the new employer as soon as possible
to make arrangements accordingly.
Rules for such situations vary greatly from university to university
so it is best to clarify things and to avoid misrepresenting yourself to the
employer. Ideally it is best to avoid such situations, but if they
can not be avoided, early planning can often result in a modification
to the position or start date that allows the process to continue mostly
as originally planned.
Another common contingency is ability to work in the country where the
position is located. In the United States it is common for the employing
institutions to provide services to foreign nationals
to secure a visa necessary to commence employment.
Yet another common contingency is approval of the position by
a higher level administrator within the university. Such statements
in offer letters can often be alluding to routine procedure, however
it is also wise to clarify this to avoid confusion as to the reality
of the offer.
Do not expect much negotiating room on postdoc offers as these
are temporary positions that are part of a fixed departmental or grant
budget.
When considering a postdoc offer, clarify whether the funding is
coming from the university or a research grant, and if the latter
what restrictions and expectations will be put on your research time.
For example, being asked to work on a targeted research project
could keep you from doing other research you'd like to do but
it could also get you exposed to higher level research ideas than you could
come up with on your own, as well as more face-time with the mentor
if they have a vested interest in the project.
For tenure track offers, salary, startup funds,
space, and initial teaching load are the most common items that are negotiated
with an offer.
The tenure clock should also be
discussed so that there are no misconceptions going into the job.
Do your homework (read the AMS Notices and Chronicle of Higher Education
statistics for example, ask colleagues what amounts are reasonable)
independently of talking to the institution making the offer.