The TARDIS "log" that Jo takes out of the upper locker and talks into is just a basic compact tape cassette in its plastic case, which became popular in the 1970s. Ridiculous and cheap, even by Dr Who standards.
It's painfully convenient that the TARDIS emergency back-up oxygen supply is in a wheeled cabinet that just happens to be right there in the console room just as the Doctor needed it.
The entry point of the Thal spacecraft looks like a 1970s back door of a terraced house.
After the Thals rescue the Doctor from the TARDIS and sit him down, the shadow of moving crew members is seen on the back of Codal (the Thal nearest to the camera).
When the Doctor recovers in the TARDIS, a crew member can be seen moving reflected in the metallic join strip of the central column of the TARDIS console.
The TARDIS runs out of oxygen because the plants outside are clogging up it's intake vents with a liquid fungus. Firstly, the TARDIS would be completely hermetically sealed anyway because it has to fly through space and exist in toxic atmospheres on alien worlds. Secondly, a ship as vast as the TARDIS would likely have an oxygen supply that could last for years, not just an hour or two. How would it be able to fly through space otherwise.