Its a Yes and No answer. 

There are 4 faults codes on an EICR: C1, C2, C3, and FI (further investigation required) 

For C1, and C2 faults you should be getting these repairing as a matter of urgency. 

For C3 codes it is up to you. Some C3 codes can require alot of alteration or swapping out of old or non compliant equipement. This can mean a rather eye watering bill for something that is only a recommendation. 

An FI will mean that you need to get the problem checked further. This is likely a fault that couldn't be identified during the safety check, but needs to be looked into to ensure it isn't something more sinister. 

Some faults are more sever than others. Alot depends on the fault that has been found and how you are using the electrical system.