Ida's hair is parted on the right. But 12 minutes into this episode, when those gathered are looking at the projected image of the planet, Ida's hair is parted on the left. Cut to the Doctor and Rose, back to Ida and now her hair is parted on the right again.
Ida, the science officer, says that the planet is in geostationary orbit around the black hole. However, the word "geostationary" applies very specifically to objects orbiting the planet Earth. Since a black hole is a type of star, this planet's orbit could be described as astrostationary, or even just stationary, but definitely not as geostationary. A science expert on an interstellar mission wouldn't make this mistake, and she wasn't dumbing things down, either, since "geostationary orbit" is already a pretty obscure topic for people unfamiliar with space technology.
When Ida estimates the ancient trap door is 30 feet in diameter, the Doctor is standing next to it. Assuming that he's about 6 feet tall, a closer estimate of the door's diameter would be 15-18 feet.
Scooti's communicator changes from left arm to right arm as she appears floating in space. You've Got the Look (2006) confirms that the f/x crew used a mirrored image.
The Doctor insists that it's impossible to orbit a black hole. However, black holes are like any other body. They can be safely orbited as long as you're far enough away or going fast enough. Close to a black hole, the orbital velocity becomes faster than light. But there's no mention that they are that close, within the event horizon.
On the night shift, Scooti is holding the wrist communicator to her face to speak, while wearing a helmet and doing maintenance work in vacuum.