The Common swipe was in regards to Com's line on the track Chi City from Be he said "My Man retired, IMA Takeover/tell these Halftime nikkas breaks over!"
In an interview he stated that that line was NOT in fact a diss and that Nas was one of the Kings Of Rap and that he would never diss him.
50 said in several interviews that the beef with Nas stemmed from him not understanding Nas's moves at the point in time coming off the Jay-Z beef. Including replacing him on the J.Lo song, Nas countered in an Allhiphop interview that he was aware that 50 was upset with him but he didn't feel the need to explain his moves to 50 and told him to get over it.
Even during their spat they both gave compliments to each other publicly, that beef was never TRULY serious, which is why neither wasted time really trying gun for the other.