There are two conditions in which you can correct a mistake on your Canadian Permanent Residence Card:
1. If the Canadian immigration department makes a mistake or miss something in your Permanent Residence, then you can apply for a reissued card. "Apply for a reissued Permanent Residence Card"
2. If it is not the mistake of the Canadian Immigration Department and it is simply some information about yourself that you would like to change such as legal name change, name change after marriage or divorce, updated signature. "Apply for a new Permanent Residence Card"
Follow the simple instructions after clicking on the above links. The application methods are straight forward and is not complicated at all.