First of all, a slight correction. Jeryn Hogarth goes by Jeri Hogarth in this series. They never mention her first name in the first episode so I assumed it was still Jeryn. I don’t have the luxury of receiving press kits so I can only base my reviews on what I see and hear in the episode itself. Sorry about the misinformation.
The second episode started off a bit slow to deal with the aftermath of the events of the first episode. That meant Jessica was being interrogated by police who apparently think she was in control of that situation or even responsible for it. In order to prove her story she first had to enlist the help of Jeri Hogarth who also doesn’t believe her side of the story. That provides the impetus of the main plot of this episode: proving that Zebediah Kilgrave exists.
Along the way Luke Cage gets involved with police and that provides the first rift in his and Jessica’s relationship. After a bit of confusion a fight ensues which gives Luke and Jessica each a glimpse of their true abilities. Towards the end of the episode Luke confronts Jessica about who they really are and it certainly seems to have repaired the rift. This is all setup for when Luke gets his own series obviously.
Kilgrave also gets his own moment to shine near the tail end of the episode once Jessica has found everything she needs including, potentially, a way to stop him. Seeing Kilgrave (from behind or silhouette, just like last episode) use his abilities to control people and how unemotional he is about everything he does was very chilling. Purple Man is not someone to take lightly which Jessica knows all too well. The problem is being able to prove it to people. Her success in this matter will presumably be determined by future episodes.
The second episode is decidedly better than the first. It provides more character development for Jessica and the supporting cast (and more hints as to Trish Walker’s possible future as masked vigilante Hellcat) and the series villain. The mystery behind how Kilgrave survived the events that Jessica assumed had killed him a year prior was well-written and paced including a hilarious undercover investigation at a hospital. They really are doing a good job balancing Jessica’s snark with the more dramatic moments of the episode. The only complaints I really have with the series so far is it’s not as good as Daredevil. However, not much is so it’s really unfair to compare them. On its own though, Jessica Jones is an excellent show so far. Hopefully everything they’ve built up so far pays off in the end. We shall soon see.