Wrong date for acquiered PR status

[nomadover9k]

Hello everyone,

I have received my permanent residence card and letter the home office normally sends with it stating the date I have acquired permanent residence status. The date in this letter is unfortunately wrong.
I came to the UK in summer 2011 and all documents I supplied where from this time. Only the employer letter had two dates in, one when I started to work for the company back at home (09/2008) and second date when I actually started to work in the England based office (summer 2011).

And regarding to the letter the resident status starts from September 2013 but actually should be from Summer 2016. So I guess the home office when by the document which was on the top of the list I sent them.

As a next step my idea was to apply for the British citizenship. Is this misunderstanding going to be a problem later? Should I report it to save the headache later?