At the end of The Thing 2011 prequel, Kate tells Sam that he's missing his earring. Sam points to the wrong ear - but if he's a perfect imitation, wouldn't he have known what ear the earring was on? Moreover, when he was assimilated in the spaceship, would he not have remembered to put the earring back on (something you can't do with metal fillings, but can with said earring)?
If the Thing's imitation of Carter had been perfect, it would indeed have had all his memories, and remembered which ear the earring was on. It therefore follows that it must not have been a perfect imitation.
Perhaps the Thing never does imitate its victims perfectly, at least when it comes to memories. Or it could be that a victim's memories just take longer to fully assimilate than their physical appearance. Carter would only have been a recent victim, after all. Had that discussion taken place a little later, perhaps the imitation wouldn't have made that mistake.