It is evitable that DVLA make mistakes time to time as they have to deal more than 40 million cars related cases each year. However, it is not funny if errors or fines due to errors happen to you, it is normal to feel upset and you can make an official complaint online by going to the following page:
emaildvla.direct.gov.uk/emaildvla/cegemail/dvla/en/feedback_
You can also write to them if you feel not comfortable to use internet. It is ensured that all the complaints filed via the above page will be investigated, and you should be able to get a reply within 2 weeks. But you need to allow additional 3-4 days for post correspondence.

If you are not happy with DVLA's decision including fines, you can report to an Independent Complaints Assessor (ICA).

In general, there are 4 steps for making a complaint. Check the following page for more: www.dft.gov.uk/dvla/contactus/How%20to%20make%20a%20complain