Mars is shown in glowing sunlight and a red-orange sky. In reality Mars has a "butterscotch" (yellow-brown) sky during the day and a pink sky at sunset and sunrise due to high levels of dust in the atmosphere.
When the Daleks invaded Earth in the episode The Stolen Earth, they were intent on destroying all of reality, except for themselves. It therefore makes no logical sense that they would just leave the young Adelaide alone instead of exterminating her or taking her aboard the Dalek crucible.
When the Doctor is telling Adelaide about her granddaughter Susie Fontana Brooke, an internet information page showing Susie's accomplishments is shown. However, the names of Susie's exploration team are actually those of Adelaide's team.
Captain Adelaide Brooke's obituary shared that her birthday was the 12 May 1999, and stated that she lost her parents after the Dalek invasion in 2008 at the age of 10. In 2008, she would have been 8 or 9.