an engineering Ph.D. teaching math in college I have a friend who has been teaching college-level math (e.g., all levels of calculus) 
for about 4 years, although all of his education, including his Ph.D., was in engineering. 
Now he is considering applying for tenure track jobs at teaching schools [edit: in the USA] and he is bemoaning the fact that nearly all the ads he sees include "Ph.D. in mathematics", rather than "Ph.D. in mathematics or related area" as a qualification. This raised a question which I don't have the experience to answer for him: are these ads, for tenure-track positions at schools that focus more on teaching, generally so serious about the Ph.D. in math that they would dismiss an application from someone with a Ph.D. in engineering instead of math? [Edit: What I have in mind here about there being a problem are legal obligations that the hiring committee would have to stick exactly to the letter, not the general spirit, of the ad. 
This is not LawyerOverflow, so examples of lawsuits over job ad wording are not necessary.]
While there are other aspects of his application which are more important for a teaching job (he gets fantastic teaching evaluations and also quickly learns how to use new educational technology), the only thing I'm wondering about on this friend's behalf is the Ph.D.-not-in-math issue and whether it's a deal breaker. [Edit: If someone knows explicit examples where it was not an issue, that would be interesting to hear about, although you can keep information about the school and the hire anonymized.]
(Of course you may ask how he got his first job teaching math and why he can't do the same thing he did then. His first teaching job was short-term, not tenure track, and his hiring had some idiosyncratic features that are unlikely to repeat themselves for the next teaching job.)
 A: In the US (I don't know if this is where you're interested), a school hiring your friend would have a bunch of added accreditation headaches if they have a non-math PhD teaching math courses. These are by no means impossible to surmount (the US system is probably more flexible than others for that), but the school would have the burden of proof; they would need to explain why this person is qualified to teach math classes, while no justification would be needed for a math PhD. Of course, having a PhD in math does not make you an expert in all areas of math, and an engineer might have interesting things to bring to the table, especially in a time of renewed interest in multidisciplinary programs, so there is a certain flaw in this double-standard system. 
As I said, these complications do not rule out a position; in practice, I have no idea if this would be considered a big deal by most schools. Smaller schools are likely to be both more flexible, but also more bothered by accreditation issues, so it might be a wash.
[PS - The best strategy for your friend is to be upfront about it, both in the cover letter and also by contacting the schools directly to find out if it's a deal-breaker or not. I suspect the answer will vary from school to school.]
A: Having been in a similar situation, I feel qualified to add in my $0.02.  My BS and MA degrees are in Math, but my PhD is in Industrial Engineering.  The easiest thing you can do is simply write the search committee and ask if a PhD in a related field is acceptable.
There are multiple advantages to this approach.  The most obvious is that they will save you time putting together a packet if the answer is no.  Additionally, you get a chance to put a bug in their ear, so that your application will not be coming out of the blue.  Finally, you will be able to trump up the advantages of having a degree in a closely related field.  In my case, many of the schools I applied to had large teacher ed programs, and I was able to tout my rather large stockpile of practical applications of just about any mathematical topic.
That said, it still can be a tough sell.  Over the course of two years, I had four on-campus interviews (one was a visiting position) without an offer.  And I was coming in having successfully written a large NSF grant, a pair of journal articles in review, and glowing teaching evaluations.
A: I guess it probably depends on the hiring procedures at each University.  I can only speak to ours. 
We give minimum and desired qualifications in our job ad.  These have to be approved by HR and the Human Rights Compliance Officer at the university.  We then screen all applications according to these criteria.  If a candidate does not meet our minimum qualifications then it would be really tough to convince HR and the HRCO that we are doing our duty as an equal opportunity employer to bring them in for an interview.  The desired qualifications allow for more interpretation on the part of the search committee, but even for this, there is a ridiculous amount of documentation and auditing that goes on to make sure that we are "fair".  
My main point is that I think that the openness on the part of the department to non-math PhDs would have to be at the ad-writing stage.  By all means, your friend should call and ask the department, if they are open to a PhD in a related field.  Just don't be surprised if they have already tied their own hands.
A: Accreditation is most likely not the reason for job postings of this sort.  The Higher Learning Commission and most State Bodies (such as Ohio Board of Regents) give universities and colleges a great deal of latitude regarding whom they hire and tenure.  It's only the professional programs involving licenses that will usually nitpick about education background:  Teacher Education, Counseling Education, Athletic Training, School Psychology, etc. etc.
From personal experience in hiring faculty members, I would say that the most likely reason why these job postings are specifying Ph.D.'s in Mathematics is that in those situations they would have a fairly good idea of what course of study the given candidate would have taken.  A Mathematics Department usually wants someone who can teach a variety of courses from the rudimentary to the specialized, and a Ph.D. in Mathematics would guarantee that the candidate personally experienced this range as a student.
Furthermore, a Mathematics Department usually wants someone with a specific mathematical research agenda, optimally one that complements their assigned teaching well.  (Actually, the interface of Teaching and Research for Faculty Positions will of course differ greatly from school to school)  The easiest way to guarantee this is to hire someone with the most obvious educational background.
That all said, I would encourage your colleague to apply for any position that they think they would be a good fit for, whether the posting specifies a math degree or not.  The worst that can happen is that they hire someone else.
A: First, a generality: in order to apply for jobs successfully, it is important to place oneself in the school's place and (try to) see things their way.
As it applies to this specific question: when schools are trying to hire on a tenure-track line, they are investing in someone for way more than just teaching, even at a teaching-heavy school. Only adjuncts are expected to simply teach, permanent faculty are relied on to shoulder some of the other tasks that make the institution go round. Specific tasks vary wildly according to the school, of course. They include, but are not limited to, 


*

*research;

*scholarship (a more general version of 1);

*administration;

*community relations;

*program development;

*scientific collaboration with existing programs/projects;

*...


[I feel like there were more items when I was composing this answer in my head. By all means please edit this answer if you can think of something I overlooked.]
Possibly counter-intuitive: the smaller the institution, the more likely that several of those things will be highly emphasized (even though the average teaching load will be higher!). 
This brings me to my main comment: what measure the success rate of an application is not if the applicant is qualified (if they're not, it's an automatic fail anyway, and there will be many qualified applicants remaining, especially these days).
The real question is: is the applicant a good fit? meaning that will they fit the needs of the institution for the non-teaching part of the job.
This is where it gets tricky: some places have a very good idea of what they need and are very upfront about it (e.g.: we need a statistician: others need not apply), in which case it's up to the applicant to prove that they fill the need. Even if your profile is not a perfect match, you have at least something to work with to make your case.
The places that do not have a specific role in mind for their hire are trickier to work with. You may think that starting from a blank slate is easier, but in my experience, it makes it very difficult to articulate one's case.
I hope this helps. I did not plan this post very thoroughly, so I want to reiterate that edits will be welcome.
A: I can comment from personal experience that my wife lost her job teaching Physics at a private 4-year (for the undergraduate degree), not-for-profit, accreditted long-standing (ancient) university in the USA (yay, Boston) with good reputation, despite her excellent teaching reviews from her undergraduate students.  They did not renew her contract in the fall just before the Accreditation Review committee was due to visit the University.
Details: she had a terminal Master of Science in Physics, followed by ten years in the defense industry, followed by a Ph.D. in a different field.  She taught as an adjunct for a few years before being offered a real position, but was let go because the perception that a Masters level in the field being taught would be seen as a negative by the accrediting board, even with a Ph.D. in a "neighboring" hard science field.  She tried to argue for her position to no avail, as they said that they could not risk losing their accreditation.  She did not want to take a step back down to teaching as an Adjunct Professor at the same institution again, so they parted ways.
It may be very difficult for your friend to get hired with a Ph.D. in an "outside" field.  It may not be just; but that is what happened.  They continue to use adjuncts to teach $>70$% of their class-load for undergraduates. 
Of course, I must add that you should always apply for a job for which you think you are qualified.
