I grew up reading 2000AD and Judge Dredd, and the snippet I just procured from an IMDb user on the Dredd page below does a good job of summing up my own theories:
If you know the story-line in the comics, what Anderson is sensing behind his need for control is his sense of doubt about the judicial system. In the comic this sense of doubt leads him to quit and head off into the Cursed Earth. That story-line about him questioning the Judge system was going to form part of the next sequel. Giving Anderson the pass even though she failed his usual high standards shows that he's considering that there might be limitations to his usual methods... (writer) Garland has said he intends to adhere to Dredd's origins as they are laid out in the comic.
I would add that Dredd is known mostly for claiming to be 'the law'. However, it is evident from the end of the film that his stance has softened slightly - he is willing to pass Anderson despite her automatic fails during the mission. This is a step towards Joe Dredd questioning the very system he upholds and this is a theme that resonates throughout the comic books. Dredd faces an eternal struggle to enforce the law he was bred to uphold, while at the same time doubting the motives of the very law-makers he serves. It is this internal struggle that Anderson detects. A chink in the armor?