... I wish they would take two seconds to explain
1. The Master's snake form and spitting thing.
2. Being half-human and why it takes a human to open the eye.
3. why the eye is in the tardis.
4. How chang and grace came back to life.
5. Why the seventh doctor just walked out of the tardis instead of just poke his head out, he can see out of the tardis and see that the tardis is being fired upon can't he?
You've got to read the book.
1. Since "Survival", the Master's been posessing alien forms to stay alive, jumping from body to body much like Jason Voorhees in "Jason Goes to Hell". The crystal-like serpent is one of the alien bodies he jumped into for convenience. Unfortunately none of them can hold him very long and they degenerate quickly. He NEEDS a Time Lord body.
2: His mother was Human all along. You just have to accept that for the continuity of this story and not worry about the rest of the series.
3: The Eye of Harmony isn't actually aboard the TARDIS, it's just a control unit that ties in to the actual one on Gallifrey. The Doctor was entrusted with this control unit because of his unique physiognomy. His retina scan reads Human, so the lock is keyed to a human pattern. So only the Doctor [or a Human] can open it. Human's are primitive apes who wouldn't understand what they're getting into, so they figure there was no danger.
4: The TARDIS is semi-scientient. It felt the same way the Doctor did about their deaths, so it used some of the left over energy from the disaster to "regenerate" them.
5: No explanation for that. Except that the Doctor is in mid-crisis. He's been forced to land and knows that the Master is on the loose. Why he stepped out at all is a question, he knows the Master is still in the TARDIS somewhere. *shrug* Chalk it up to plot requirement theater.
More dramatic plotholes in the movie to address are why the Daleks agree to let the Doctor come and pick up the Master's remains in the first place! But the book covers that too. He wasn't permitted, he slipped in quietly and stole them after the Master sent him a telepathic plea to take him home.
Why does the 'Eye' only allow the Master and Chang see the last incarnation and not all 8?
In the book, they see all of them.
Why doesn't the Master have his famous goatee when he possesses the paramedic like he did when he posessed Tremas?
Eric Roberts refused.
Why does the Doctor kiss Grace?
Trying to appeal to a new US audience who expects this kind of crap.