Capacitor in parallel with resistor on xoscope amplifier schematic
My guess is that the designer is bypassing the series resistor in an attempt to mitigate the frequency roll-off caused by the diode capacitances of D1, D2 and D3.  D1 and D2 are reversed biased, so there's the drift capacitance, and D8 is forward biased, so there's diffusion capacitance.  Added together in parallel they might combine to give (just a guess) 20 pF of capacitance.  That forms a low-pass filter in combination with R2, and without C3 would limit the bandwidth to about 170kHz.  The TL084 has a gain-bandwidth product of 4 MHz, and with a gain of ten would have a bandwidth of about 400 kHz, so in this configuration it can do better.  

I guess the designer is assuming(?) that at high frequency the source will be current limited and that the op amps own internal ESD protection will handle things; this circuit seems mainly designed to protect the input if, say, it's connected to an audio amp putting out 40 volts p2p.  

C1 should definitely be moved; R1 and C2 are there because they are to be matched to the source impedance of the probe, and C1 will mess up the response!