Perhaps my memory is fading, but I don't recall any of the previous incarnations coming up with a line like "Do you mind not farting while I'm saving the world". Even so, the first three episodes have set a pretty high standard, although if you remember the first ones, with William Hartnell the bar isn't set especially high!
Billy Piper, who was good in Canterbury Tales is good here too with the right mixture of pliant sidekick and sex. Not so much flesh as Leela (Louise Jameson) but there is time yet!