I'm on like the 10th episode of Travelers. It's a neat concept, and I like what they've done with it, but it's far from airtight. Slightly spoiler-y with concepts that become apparent early on but major spoilers are hidden.
The issues I have are mostly related to increased drama. If these problems didn't exist, then the show would be more boring, so I get why they did these things, but I feel like the writers could've done something different with them.
First off, I'd imagine that it'd be easier to teach the travelers to cut themselves off from their hosts' former lives. Let the divorce happen. Emancipate the teenager. Leaving these people in their families' lives would impact the future, so just let the drifting away happen. Of course, that's really tricky to do with the entire family of travelers whose daughter wasn't taken over. After all, good luck not getting thrown in jail for abandoning your child.
But while that policy makes emotionless sense, it is perfectly understandable why Carly cannot just give up her baby. There was no emotional attachment to the baby at first, but any decent human being wouldn't be okay with leaving the baby with the father. So even though it's truer to the original timeline, she can't let that happen.
But yeah, for all their talk of preserving the future as best they can, they're sure doing a great job of changing it by still being in their families' lives.
But I can forgive those. They do provide more drama, and it makes sense that humans would want to form bonds with other humans. The issue that bugs me because of its artificial drama is episode 6 with the antimatter beam being put in place. The elderly reinforcements follow that nonkilling protocol so closely that they do not kill any of the soldiers. Even though their actions will result in the soldiers' deaths anyway, they hold back and end up letting Major Gleeson threaten to jeopardize the mission.
But aside from those, I am enjoying the show.