The EQE curve typically resembles  the absorption spectra of the dye you used and be also affected the structure of anode you used (light-dye interaction, light harvesting). If you have abrupt peaks from your measurement, I think there is possible problem on the contact for probing you cell. If you measure EQE using laser beam induced current (LBIC) to obtain 2D EQE map, some abrupt peaks may arise from the inhomogenity of your cells or from defect fabrication (e.g. hole, cracks, etc).

Be careful when exposing DSSC to chopped light - some of the internal time constants especially at low terminal voltages are extremely long - hours or days even. Make sure that the cell is carrying current to discharge the large self capacitances. In terms of behaviour Ruri has surely listed most if not all of the possibilities. Can you upload one or two graphs please?

the chopping frequency should be lower than 1Hz for this performance ( 2mA/cm2), The EQE of DSSC more sensitive at high chopping frequency. 

 EQE is measured against a reference cell under current conditions, so I will measure my cell exactly against the reference just measured. If i remember correctly when i was using a system with chopping frequency it was always set at 50Hz, without any problem. It might change with the instrument manufacturer. And most of the time calling the manufacturer technician really helps.