When this happens, what does your Vcc read.
The pins on the PCF8574 can only source 100 µA.
When the PCF8574 outputs 1s, the voltage at its output reads 4V
Check to see if there's a voltage difference between the ULN2803's ground and other ground points.
Have you got decoupling capacitors close to your supply pins of ic's?And are your ic's etc grounds all connected to the same 'gnd'?Also... if the pcf8574 is configured for 'outputs'..... then external pullup resistors aren't required, right?
P6 and P7 on the PCF8574T are net named as +LED1 and +LED2. The circuit for these LEDs isn't shown, but it implies that you're trying to source LED current when you should be sinking LED current instead. Also, the LED current limiting resistors (not shown) would need to limit the current to within 10mA.
The required pullup resistors for SDA, SCL and INT are not shown. What is their value?
Typically your indicator leds would be on the ULN2803As outputs...
Perhaps your 10K pullups could be a bit stronger (i.e. 3.3K - 4.7K).