I am fairly skeptical about the two versions of the question, namely weather whether mathematicians have much to learn from habits in other academic disciplines regarding how to do mathematics, and also about the suggestion that mathematician tend to use "mathematical habits of thought" which are unsuitable in other areas.
Regarding the first question: of course, I think it can be very beneficial for mathematicians to learn "habits of thoughts" in other academic disciplines, as well as in other areas of mathematics. And having wide horizons can be, at times, beneficial also in one's own research. Adopting blindly habits of thought from other areas into mathematics (or the other way around) is not a good idea although here and there it can be useful.
Specifically, to the suggestions regarding the first question: Technical difficulty and complexity is indeed often a sign of quality, and there is appreciation also for simplicity. It is interesting if heuristic and nonrigorous methods can be of more use in pure mathematics. But one should be rather cautious about them. To some extents they exist e.g. in making conjectures. Certainly they are central and important in applied mathematics. Heavier use of computers is a nice idea, and it raises interesting question about the nature of mathematics and mathematical understanding. But the progress is rather slow and there is no good evidence for the bold prophecies regarding much more central role to computers in general, and automatic theorem proving in particular. It is not clear at all if debates and discussions regarding mathematics can be useful as they are in other areas.
Regarding the second question. I dont see any evidence that mathematicians use improperly in a noticable way "mathematical habits of thoughts" when they are uncalled for. Of course mathematicians vastly differ in the way they handle nonmathematical issues (and there are different approaches among mathematicians to mathematics as well).
Specifically, I do not understand the suggestion about ambiguity; I dont think mathematicians are less open to opinions compared to others, I dont think nonmathematicians are better (or worse) in dealing with shades of grey. I dont know to what extent "the best people alive cannot add fractions", and the advantages and disadvantages of oversimplified model is a very central issue in mathematics as in other areas.