The two diodes across R1 are there to protect the OP-AMP from voltage spikes due to any large transients in the measured current.
The R-C network on the output is there to give a smooth DC output. The output from the op-amps will be halfwave pulses, not very usefull for reading with an ADC.
Look at the last paragraph of the application note.
It clearly states that the RC network should have a time constant which is at least 10 times greater than the period of the measured current.
So for a 50hz current, the period is 20ms, then make the time constant greater than 200ms.
JimB