As I understand it, “it depends”. Old code may have things that assume 32 bit without being explicit about it (or checks if things behave within boundaries), because 64 bit was never a real option when the code was written. Some not-so-strict programming that would mostly work for its purpose in 32 bit, may fail in 64 bit. These are the things that may break without clear cause, and those errors may be hard to track down.

Some programs rely on 3rd party code (internal routines or external plugins) that is 32 bit. Maybe that 3rd party code is not (freely) available to also be converted to 64 bit. Such things could mean the end for certain features.

Converting Your App to a 64-Bit Binary at developer.apple.com