are there circumstances where a developer should compile their products with more than one compiler to flush out issues, potentially fine tune/optimize code, etc? I've never thought about doing this.
Yes, at least make sure that your code compiles and the tests pass on more than one. That way you're sure that you're not depending on peculiars of one compiler (their specific behaviors that are undefined in the standard, optimizer actions, etc).
At a previous job we ensured we got clean compiles with Visual C++, SPARCworks and xlc, even tho' all our customers were only actually interested in the Solaris version.
When I was working on multi-platform console engines, I had no choice but to compile with several highly varying compilers. It teaches you very quickly how quietly compiler-specific extensions and quirks work their way into your code.
Also, different dev environments offer different tools. A nice benefit of running in lots of environments was that I often could pick between the best tools of any platform whenever I had a problem they could help solve.
Yes; whenever they want to produce a higher quality product. Which I'd anticipate being "whenever possible", limited only by compiler extensions one has to use, and dev/target hardware.
I've worked at places where we maintained a dual build, VisualC++ and Linux gcc, because we wanted to be able to develop and run in multiple environments. That forces you to write clean standard-compliant code, although in some cases it could be a pain.
