Like most programming techniques, nested functions should be used when and only when they are appropriate.
You aren't forced to use this aspect, but if you want, nested functions reduce the need to pass parameters by directly accessing their containing function's local variables. That's convenient. Careful use of "invisible" parameters can improve readability. Careless use can make code much more opaque.
Avoiding some or all parameters makes it harder to reuse a nested function elsewhere because any new containing function would have to declare those same variables. Reuse is usually good, but many functions will never be reused so it often doesn't matter.
Since a variable's type is inherited along with its name, reusing nested functions can give you inexpensive polymorphism, like a limited and primitive version of templates.
Using nested functions also introduces the danger of bugs if a function unintentionally accesses or changes one of its container's variables. Imagine a for loop containing a call to a nested function containing a for loop using the same index without a local declaration. If I were designing a language, I would include nested functions but require an "inherit x" or "inherit const x" declaration to make it more obvious what's happening and to avoid unintended inheritance and modification.
There are several other uses, but maybe the most important thing nested functions do is allow internal helper functions that are not visible externally, an extension to C's and C++'s static not extern functions or to C++'s private not public functions. Having two levels of encapsulation is better than one. It also allows local overloading of function names, so you don't need long names describing what type each one works on.
There are internal complications when a containing function stores a pointer to a contained function, and when multiple levels of nesting are allowed, but compiler writers have been dealing with those issues for over half a century. There are no technical issues making it harder to add to C++ than to C, but the benefits are less.
Portability is important, but gcc is available in many environments, and at least one other family of compilers supports nested functions - IBM's xlc available on AIX, Linux on PowerPC, Linux on BlueGene, Linux on Cell, and z/OS. See
http://publib.boulder.ibm.com/infocenter/comphelp/v8v101index.jsp?topic=%2Fcom.ibm.xlcpp8a.doc%2Flanguage%2Fref%2Fnested_functions.htm
Nested functions are available in some new (eg, Python) and many more traditional languages, including Ada, Pascal, Fortran, PL/I, PL/IX, Algol and COBOL. C++ even has two restricted versions - methods in a local class can access its containing function's static (but not auto) variables, and methods in any class can access static class data members and methods. The upcoming C++ standard has lamda functions, which are really anonymous nested functions. So the programming world has lots of experience pro and con with them.
Nested functions are useful but take care. Always use any features and tools where they help, not where they hurt.