If they pick up where they left off, it will look like Duke slipped out for a haircut in between cradling a dying Jennifer and confronting an evil Mara.
They could do like they did between seasons 2 and 3, where they reshot the cliffhanger scene for the "previously" sequence. In the season 2 finale, Duke has short hair. In the same scene in the "previously on Haven" recap leading into the season 3 premiere, Duke has longer hair and a ponytail (there seem to be some other differences, but I haven't done a real comparison). So we could see that last scene again, but with a short-haired Duke cradling a dying Jennifer. Or, since suddenly short hair is easier to explain than suddenly long hair, they could use a wig for the cliffhanger conclusion, then the next time we see Duke he has short hair and Nathan makes a remark about his haircut.
After an Olympics break, back to the rewatch. There's not much in "Fur" of long-term consequence, though I did find it interesting that Jess describes the Troubles as being the result of magic. It seemed at the time that she was just being fanciful (and flirting with Nathan), but I guess she turned out to be right.
The thing that struck me this time around is how annoying I find the Chief here. His constant gripe to and about Nathan is that he doesn't see what's in front of him -- mostly meaning that he's in denial about the Troubles -- and yet here Nathan spends the whole episode arguring to his father that this isn't an ordinary animal attack and going wolf hunting isn't the answer, only to have his father scoff and sneer at him. If Nathan got mocked and criticized when he did see what was in front of him, then no wonder he was in denial, at least publicly. It didn't seem like he was truly in denial, though, even if he did go to the doctor when he started feeling. It would be interesting to know how he dealt with things before Audrey's arrival, but once he was sure that Audrey wasn't going to bring the government black helicopters to town if she knew there was really paranormal stuff happening, he was right there with her in acknowledging and figuring out the weird stuff. His failing was in not standing up for himself to his father/boss about what he saw. I guess maybe that's what the Chief was hoping for, but if Nathan grew up seeing his father pretending to him that the Troubles didn't exist, you can hardly expect him to be presenting Troubles explanations for events when his father is his boss.