At work, going from 16-bits to 32-bits meant moving from the PDP-11 platform to the VAX-11 platform. The biggest difference there was not so much the BASIC, FORTRAN, or COBOL program, it was changing the Link options to go from Overlays to Virtual Memory. After that, you could eliminate a lot of the common areas you needed so you could swap program sections in and out of memory since the VMS operating system took care of the Virtual memory management. Same thing with moving to 64-bit code on Alpha (and Itanium) but there the Architectural differences were more significant going from a CISC CPU to a RISC CPU. Memory Page sizes changed, as did integer boundaries, being aligned to longwords instead of words or bytes.
I've got a number of 32 bit Apps on my iPhone, so I guess I need to clean house, too. Like Hall mentioned, updates have not been done for several years in some cases.