Why is this opto isolator input turning off so slowly?
There is some capacitance associated with the input. When the transistor turns off, this capacitance must be discharged through the LED of opto. As the data sheet suggests, at an input of about 1.5 volts the LED will turn off, and the output will switch. As you have determined, this takes about 3 usec, and you should compare this to the output delay. (Hint: they are pretty close to the same.)

Once the voltage drops below about 1.5 volts, the exponential nature of LED voltage/current means that the LED will start drawing less current, and rate of voltage drop will be reduced. At very low voltages the current will become very low indeed. This will lead to a long "tail" on the input voltage, as you see.

Try adding a 1k resistor from the input to ground, and see if that doesn't speed things up. There is no need to do this for an operational circuit, since it only cares about the voltage above about 1.5 volts, but try it anyways just to see what happens.