The biggest changes seems to be in intuition and graphics library, whereas DOS and exec are pretty much the same for most applications.
Uhum. KS 1.3 dos.library is anemic compared to KS 2.0+ one. So as a rule of thumb unless if the application uses stdio it won't work with KS 1.3.
Even exec library has tons of new stuff, such as AllocVec/FreeVec which are used extensively in newer programs. It is quite unlikely you could take some even remotely modern amiga application and build it easily for KS 1.3.
