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1. Vbat - should be connected to GND if is not used (if Vbat is not present, DS1307 will not keep calendar data when the board is unpowered)
2. SOUT - is an open collector output, it should have a pull-up resistor
3. DS1307 uses a 32.768 kHz crystal and not requires external capacitors
In the simulation, the VBAT pin wouldn't affect the simulation. But in real hardware, you need to connect a 3V battery from VBAT to ground (for battery backup) or connect VBAT to ground to have the DS1307 working without battery backup.
The SOUT pin is not used, so the pull-up resistor isn't needed.
As pointed out by cristianp, C3 and C4 are not required.
For the LEDs, you need to use current-limiting resistors. Connect resistors between the PORTD pins and the LED anodes to limit the current. You have to choose resistors to allow a maximum current of 20mA (provided these are standard LEDs). 10mA is enough current.
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