Continuity mistake: In the side mission Creature Of The Night, Francine Langstrom is shown as deceased in Batman's detective mode, so there's no way she can be alive later as shown.
Continuity mistake: In both Arkham Origins and Arkham City Mr Freeze is bald. Yet here he's shown to have strands of white hair in the DLC mission In From The Cold.
Continuity mistake: This takes place a year or so after Arkham City. Yet Joker's Titan poisoning marks look different, more like blood stains.
Continuity mistake: This is in the same universe as the other Arkham games yet Poison Ivy's gone from being green in Arkham Asylum and Arkham City to being just regular looking in this game.
Continuity mistake: When you find Gordon in the mall he's wearing his jacket. When you rescue him just after your final fight with The Arkham Knight he's not. Then he's got it back later at the asylum.
Answer: As a child, Jervis Tetch never had any friends. Even in his adult years, he was all alone. When Jervis asked Batman to be his Alice, he was essentially asking Batman to be his friend.