In the 1980 scene at 26:20 the kids are watching "Blake's 7" a British science fiction series that ran from 1977 to 1981 in the UK.
Unlike many historical dramas, the depiction of Saratoga is reasonably accurate. The shot of the American camp corresponds reasonably well to the real world geography, including showing the mountain across the river in what's now Washington County. Morgan's men really did take part in the opening events of the first battle and, contrary to Claire's hope that the sharpshooters would remain in the rear, were part of a direct frontal clash with the British.
In an interview Richard Rankin and Sophie Skelton talk about the dinner scene and how since they had to do it several times at first the actress playing their daughter Mandy said she didn't like the food, but after a couple takes she decided it wasn't so bad.