As much as I enjoy the program, as well as Frequency on the CW, certain things bother me. It is pretty clear in the first episode, that changing the history of the Hindenburg will have an effect on history with all those who died, now living. However, they've implied that other events did not have a major impact. I would disagree because of the ripples likely caused by the actions of both sides. Two episodes in particular stand out.
The assassination of Lincoln planted seeds in the minds of many that the CSA played a role in the plot. In some way it could be argued that rounding up all the conspirators might dispel that belief. However, now you have a history in which a mysterious killer slays the President, escapes, and is never found. This might have the effect of the Union being more harsh towards the South after the war, with people thinking even more strongly the CSA had a deeper role in the plot and the assassin was a Confederate agent.
In the Alamo story, Santa Anna shows no mercy to those in the Alamo and announces he will kill everyone, women and children included. Despite the escape of the women and children, thanks to the time travelers, I think this might inspire Texans to be more brutal towards Mexico and less likely to take survivors at the Battle of San Jacinto.
I've always leaned somewhat to the theory that literally traveling in time alters time to some effect.