Theory:Doctor Who television discontinuity and plot holes/Utopia

• At the end of DW:Last of the Time Lords, Jack says that he can't die but he still keeps getting older. In this episode, he claims that his vortex manipulator went wrong and he was forced to live through the nineteenth and twentieth century. How come he has not aged?

He has. Compare this Jack to the one in Series 1. The rate at which Jack ages is simply much, much slower than normal human aging. Also, the Doctor earlier asked if Jack had had "work done".

• Before the guards would let the Doctor, Martha and Jack into the silo, they yelled at them to show their teeth, in order to make sure they where not Futurekind. So, how did the female Futurekind, who tries to sabotage the shuttle launch get in?

Either that individual snuck in, or perhaps this could be a hint to the development of humans into Futurekind as referenced by Professor Yana.

• Jack hears Martha referring to the Face of Boe's last words but makes no connection with that being his own youthful nickname or wonder if there is a connection and also he doesn't flinch when Martha mentioned the name.

He likely didn't hear it, and/or chose not to bring this up at that point - considering the depth of explanation needed and considering and that they were rather busy.

• Jack is able to grab onto the TARDIS when it dematerializes, yet when others have attempted to in some way maintain contact with the TARDIS as it disappears, they are unable to (see, for example, Sally Sparrow and Larry Nightingale in DW:Blink.'

The series has never been consistent in the mechanics of the TARDIS dematerializing. Perhaps there is a specific point in the dematerialization at which someone may hold on to the Tardis and dematerialize with it, and Jack is the first to reach it by that point. Also, we don't know if the TARDIS actually faded away or if it took off vertically without dematerialising as established in The Runaway Bride. The reason Sally Sparrow and Larry Nightingale couldn’t hold onto the TARDIS as it left is possibly due to the Authorized Control Disk telling the TARDIS to leave them behind (No need to bring them to 1969!). Perhaps there are Emergency Programs other than Emergency Program 1 (which takes the occupant home immediately) which force the TARDIS to evacuate without the occupants.

• Jack shouts "DOCTOR!" while clinging to the TARDIS. Is there air in the time vortex?

Jack only shouts 'Doctor' once. That would only take one breath, which he certainly had in his lungs.

• It is left unclear why none of the Time Lords during the last Time War against the Daleks tried to use the Time Vortex to destroy the Daleks. If a Time Lord looked into the Time Vortex he or she would become a god, a vengeful god, as mentioned by the Doctor in this episode. This would be incredibly dangerous. It is implied in DW: The Christmas Invasion that Time allowed Rose to do what she did as a singular event; none of the Time Lords may have been allowed such an opportunity. As well, the Dalek Empire they were facing was far more powerful and extensive and could have countermeasures to such an attack. Also, the last few days of the Time War were supposedly hell, and the possibility of both sides using such power could well account for that. Rose was the only one with such power at the time, while during the war if competing entities such as that could have effects less one sided.
• According to the Doctor in DW: Rise of the Cybermen his TARDIS is the last in the Universe, so how did the Master travel to the End of the Universe?

Having access to Time Lord technology when he decided to run from the Daleks, the Master would have had multiple technological options to send himself to the end of the Universe.

• How come refueling the Tardis in DW: Utopia takes 20 seconds but in DW: Boom Town it takes a whole day?

The Doctor references that the rift has been active, which obviously allows the process to happen much more quickly.

• If the Time Lords have never been that far in the future, how does the Doctor know that that is the 'end of the universe'?

The Doctor must have recognised that the TARDIS stopped at the year 100 trillion because it could go no further into the future, the end of the line so to speak. Additionally, its highly possible that the Time Lords knew about the end of the universe, with all their knowledge of time travel, but simply had no cause to go there.

• The Master is now human, yet he starts to remember his Time Lord self. How is it possible that when the Doctor and the Master became human, their minds did not burn up like Donna's would if she ever remembered everything that had happened while she had traveled with the Doctor.

Donna was specified to have a Time Lord consciousness in a human mind, while the Doctor and Master became human and lost their Time Lord consciousness. Donna was the only one to try to have both at the same time.

• The Master regenerates while concious, accompanied by a huge discharge of brightly coloured energy, similar to the Ninth Doctor in [The_Parting_of_the_Ways|DW: The Parting of the Ways]. The Ninth Doctor implies that the only reason for the violence of this type of regeneration is that he has absorbed the energy of the time vortex, but this has not happened to the Master.

The ninth doctor never actually says that the time energy causes his regeneration to be violent, and besides, look at the tenth doctor's regeneration(s). Neither involved the time vortex and yet both were, at least, as violent as that of the ninth doctor (in fact, his regeneration into the eleventh doctor was considerably more violent, so much so that it almost destroyed the TARDIS).