pert:
If your code does not use the USB capabilities, then it will work on the Uno
...unless you are using some hardware capability of the Leonardo pins that does not exist or is in a different place on the UNO. For example the Wire pins are A4 and A5 on the UNO and digital 2 and 3 on the Leonardo. The Leonardo has external interrupts on pins 0, 1, and 7, in addition to pins 2 and 3 like on the UNO. The Leonardo has 6 additional analog input pins (A6-A11) on digital pins 4, 6, 8, 9, 10, and 12. The SPI interface is only available on the ICSP header and not on digital pins 10 through 13 like on the UNO.