7. The Shakespeare Code
In the second episode of series 3 with Martha, The Doctor and Martha visit the Globe Theater in 1599 to attend a performance of William Shakespeare's Love's Labors Lost. In the episode, the duo and Shakespeare encounter three witches that are trying to restore their imprisoned population through the power of Shakespeare's words. The witches, actually members of an alien race called Carrionites that use and thrive on the power of words, attempt to use Shakespeare to finish his lost play Love's Labors Won, and have it performed the next day to complete their task.
When He Should Have Regenerated: The witches use voodoo dolls and strands of human hair to kill some of their victims. The Doctor calls the doll and hair combination a DNA replication module as opposed to magic, and when one of the Carrionites takes his hair and combines it with the doll, she stabs him in the heart. While the Doctor has two hearts and one was left intact, he is unable to function with only one, which we witness in the seventh series in The Power of Three. Earlier in the episode, a character died when the Carrionites drowned and stabbed his voodoo doll, and exhibited outward symptoms of the drowning, having water come spouting out of his mouth uncontrollably as a visual queue. This means that his heart was likely penetrated as well, though no outward signs could be seen of this. So, when one of the Doctor's hearts was stabbed, it should have resulted in his eventual death by internal bleeding and lack of required circulatory function. However, with a little guidance, Martha was able to save him by hitting him in various places over the heart to jolt it into functioning. What this proves is that not only is there a lack of continuity to the way the voodoo dolls function in this episode, but that Martha is a terrible medical student who shouldn't have assumed the Doctor's idea for restarting his heart would work.