Yes, there will be problems regarding registration.
If not, people would just transfer programs to multiple computers without purchasing separate licences.
However, in the case of certain programs, like MS Office, the program can be uninstalled from one computer and installed on a totally different computer. I have done this successfully. In every case, I uninstalled the program first; then installed it and registered it on another computer. This is also possible on Windows OS with the Retail licence; not the OEM. (I know you are referring to a Mac).
Each licence is different; depends on the EULA.