I know all the times I find those stupid similiarities, but you can hear a small similiarity between the opening melodies of Papercut & Part of Me...with a slight difference in the octaves...
The only similiarity that I see in POM is how Mike's raps are similiar to APFMH - as in he raps them fast and on the second verse, the first line is rapped with no guitars or whatever and then they come in. I need a life, sorry.