There are 7 Doctors, as one can plainly see from the backglass… quite conveniently, they are numbered 1-7. Each Doctor has the effect of changing the rules of one area of the Playfield, making a list of the rules all the more annoying and probably confusing.
First some general information about the Doctors… there are many ways to “spot” doctors throughout the game – one is awarded at the start of any ball, and can be spotted through the Transmat target or Video Mode. At the start of a ball (or when a ball has been locked), you get to choose the “current” doctor – his picture will flash on the backglass. When a doctor- spotting shot is made, the current doctor will become solidly lit (so his attributes are carried over for the rest of the game), and the “current” doctor becomes the previously unlit doctor directly to the left of the previous one.
There are 2 ways to spot all seven doctors – either go through them all one-by-one, or shoot the Emperor Daleks jackpot. Either way, all of them will be lit for the rest of the game, and you receive an additional bonus of 2OM, as well as a small animation, which plays even after a tilt! After all 7 doctors are spotted, they can be spotted a second (third, etc) time, and running through all 7 a second time awards another 2OM bonus. Also, each doctor spotted in the game (this count may be more than 7) is worth a 1M bonus at the end of the last ball (so don’t tilt it!), and this bonus (unlike the regular bonus) is multiplied by the Playfield X.