It is really easy to interface the ds1307 in C or C++, and there are plenty of examples, so why do you want to use assembly?
If the purpose is just to learn machine language programming, do something simpler to start with. It is extremely unlikely that someone will be willing to read through your assembly program and correct it.
Using a logic analyser would also help in debugging this. There could be timing issues involved. Or you could atleast check what the I2C device returns based on what you feed it. And in what pattern the leds light up.
At the very least I suggest you add code routines to send the I2C state and received data to the UART port as debug information.