When Wilma Deering gets into her fighter on board the Draconia, her helmet is marked 'Col. Deering' on the right side. In the subsequent shots during the fight, it's unmarked. A similar thing happens again close to the end of the film: When getting picking up Buck, Theo an Twiki on the Draconia, there is one shot of her with her helmet being marked 'Col Deering' - this time on the left side - whereas in all other shots the helmet is clean.
The length of Buck's hair changes between shots. Particularly when he is first shown his new apartment, his hair is a little shorter than the scenes before and after it (these scenes were filmed months later for the TV version).
Buck says that the weapons fire on his ship had not oxidized and therefore was new, but oxidation requires oxygen which cannot happen in space.
In the first two episodes (Awakening - Parts 1 and 2) the year of production at the end of the credits is incorrectly marked as MCMLXXVIX, which does not correctly equate to any full number in Roman numerals. This was corrected in the subsequent episodes produced in 1979 to MCMLXXIX.
The opening narration states that Capt. Rogers' ship was launched in 1987. But the launch is of a Saturn V rocket, which was last used in 1973.
Buck Rogers has been asleep for over 500 years yet wakes up with a clean shave. However, it is made clear that Buck was frozen in his ship for that period, akin to suspended animation and not simply asleep. It makes sense that his hair and beard would not grow in that time.
During the space battle Buck pulls back on the stick but the Starfighter flips to the left.
Draconia is described as a "dynasty that has conquered three fourths of the universe." Earth is sparsely populated and still recovering from a global nuclear holocaust. Yet the Draconians and the Earth forces are portrayed as an even match militarily.
In the scene where Buck is awaiting execution, he is talking with Col. Deering and she tells him that she is there to give him a chance to prove he is innocent. A boom microphone is visible above them for a few moments. The scene changes and goes back and the microphone is no longer seen. This is at 41:39.
When Wilma tells the other pilots to not use their combat computers, one pilot is shown turning the computer off. He presses the Evade button instead of the Override button Buck used earlier.
Theo addresses Princess Ardala as Your Majesty/Her Majesty. However, only a monarch (a king or queen) is addressed as "majesty". A princess would be addressed as Your Highness/Her Highness.