Here are pictures of those two I said I have like yours - on closer inspection (by digital microscope) they are R letters after all and not P as first thought. Depends on viewing angle sometimes.
First picture from a distance looks like they are PEMEMBER and then second and third closer pictures show REMEMBER word. Click to enlarge to see detail.
I also have the normal non-commemorative £2 coin which has a broken/worn letter T where the lettering STANDING ON THE SHOULDERS OF GIANTS has just the top half of T in the THE word in lettering. So broken letters are common for the £2 coin. Plus when the letters are stamped in the coin there is black colour added to make it stand out more, and sometimes the colouring is not there.

Above shows I put six of them together with rubber band temporarily, and the top three (older coins 2007 2008 2011) actually now I see have similar errors, as mentioned above, and the lower three are more recent coins (all 2013), so the Mint have learned it seems. That lowest coin has lettering almost off the edge I just noticed !
I did have a 1999 Rugby commemorative £2 where in the edge lettering the 1999 date had what looked like a missing 1 number so appeared to commemorate the year 999 instead. I have heard of (but never seen) the GIANTS lettering having a missing I so looks like G ANTS. And so on ...!
EDIT: In April 2015 I add this link shown to me by a member, rather than create a reply ...
http://www.fireworks.co.uk/pemember-coin.html