In the sequence where Darren McGavin character Sam Parkhill and his wife are trying to evade the Martians on the Sand Ships their scenes the background sky is Blue & Cloudy but when it switches to the Martians the skies are Dark sandy brown.
Addition to the already stated goof regarding communications with Earth. Since the Earth revolves around the sun twice as fast as Mars the gap in communications between Earth and Mars would increase a little every day. In fact, when Earth and Mars are at opposite ends of their orbit (farthest away from each other) the gap in communications between the two planets would take somewhere around 20 to 25 minutes. Not only that, when they are at their farthest distance apart the Sun would be between the two planets. That would probably result in a communications blackout that would last perhaps several weeks before the Earth could travel far enough in its orbit to avoid the Sun's interference with radio waves.
The couple at the remote diner look at the Earth through a telescope at night (stars in the background). This is impossible since Earth's orbit is inside the orbit of Mars. But in fact it is exactly the same as viewing Venus and Mercury from Earth, which is perfectly possible at night. When the sun has just set, one can see objects that are in the sun's vicinity. Just like Venus is visible from Earth, both Earth and the Moon are visible from Mars as evening or morning stars.