Compiling source code on Linux Mint can fail with the error "C compiler cannot create executables," often due to missing permissions or required packages. Users are advised to check the exact error message and review the config.log for more details. Installing both gcc and g++ is essential, and the command "apt-get install build-essential" can resolve missing dependencies. Running the compilation command with superuser privileges using sudo may also help. Ensuring proper setup and permissions is crucial for successful compilation.