Ellie is clearly played by a male German Shepherd. Female German Shepherds come in brighter coats than males and often lack the black streak across the forehead.
In one of the scenes the dog is watching "Dynasty" in the 80's on an analog TV and noting that the protagonists are fighting. Dogs could not recognize images on analog TVs, as their eyes could recognize the flicker effect that happened with analog images. It wasn't until digital TV came along in the 90's that dogs could recognize images on TV.
In 1961 or '2, Ethan is shown reading an apparently new issue of Captain America. This series had been out of print since 1953, until it was revived by Marvel Comics in 1964.
One of the themes is that Bailey is reincarnated into a new life almost right after he's died in the previous life. The issue here is that each time he's reincarnated, multiple years have passed since his prior life. When he's reincarnated it should be instantaneous instead of several years passing.