If they succeed.. (spoilers)
..(either their group or some of the other thousands of travelers they mentioned) how will they be able to go back in time... in order to succeed? This is an extended version of the Grandfather Paradox, which is already obvious that will plague this show, as has already plagued other shows such as 12 Monkeys (which I abandoned in early - mind Season 2, when it became too much of a mess) and already appears to be an issue with Timeless.
It does not really matter if they are five of them, 5000 of them or 5 million of them. The paradox applies equally, and you cannot dilute it with a high number of missions. So, the entire concept of the show is based on a glaring paradox, unless they do not succeed of course.
They also confused the original timeline with the new timeline. How/why would the FBI agent fall to his death originally if they had not lured him into that building? If they already knew he would die because of their invitation then they are responsible for his death, which contradicts their "do not affect the timeline" and "only get bodies that were about to die anyway" mantra (which has not been spelled out yet, but it was strongly suggested by the junkie's reluctance to help the detective "because he was supposed to die").
A recent time travel show I watched which had no obvious paradoxes is "Frequency". I've only yet watched the pilot, but I believe they handled the plot quite gracefully.
Fanboy : a person who does not think while watching.share