So Milner's washing his face in a stream when Jim shows up and casually draws out of him that he didn't really kill Foster, but that he confessed to protect Rebecca, who he thinks did kill Foster, and that he assumed Taylor would commute the sentence.
So Jim puts a baseball cap and a hoodie on Milner to march him, implausibly, right back in to Terra Nova back to his house, where he confronts Rebecca. All Rebecca has to do is say she didn't kill Foster, and that's good enough for Milner and Jim. She says she was glad when Foster ended it, because he turned out to be a jerk, preferring his friends and his gambling to her. I'm shocked that someone who would bone another man's wife turned out to be not such a great guy!
So Taylor's pissed that maybe he sent the wrong guy out to be banished, because he put his own reputation on the line to do so, but Jim says they have another lead, and Taylor wants it locked down because Jim's gut is "not good enough this time." Or ever, really, if you want this to be a worthy society.
Meanwhile, this stupid ankylosaur plot is going on, with Elisabeth doing laser surgery through the shell with Malcolm and his perpetual hard-on talking about how great she is and saying dickish sabotage things about how Jim should be there to watch her artistic surgery genius at work, and Elisabeth resignedly says Jim's probably got something better to do, and I actually do think that preventing an innocent man's death by banishment is just a little more important than helping the stupid dinosaur fetus.
Anyway, the gambling business -- going on at Boylan's -- has Jim thinking that maybe he and Washington should be looking at, what's the word, oh yeah! EVIDENCE, so they check out Foster's financials. "Look who owed Foster a lot of money," says Washington, so they take it to Taylor, and then the three of them plus soldiers descend on Boylan's to arrest the guy. Taylor gleefully says he's been waiting a long time to take this guy in, which is kind of confusing given that Taylor seems to have absolute power in this place. This is also when Jim finds out that his own flesh and blood is working at the drinking and gambling den, and threatens to talk to his son later.
So: interrogation of Boylan, with soldiers guarding the door. Taylor threatens to shut down his place unless he comes clean about the gambling at his place, and Boylan laughs it off, saying the colonists wouldn't stand for it. Jim says that when they were going through the financials they discovered (somehow, I guess?) that Boylan keeps old-school paper records, and when they find them, that's all they'll need to draw the connection to Foster. Boylan's a little less cocksure when he learns they think he killed Foster.