Are the last drips after pulling an espresso less tasty? Someone told me that the last drips coming out of a espresso machine after the pull is finished (when there is no water pressure any more) contain bad flavors. He recommended that I remove the coffee cup in the moment the machine stops producing pressure.

Is that true? If yes, why?
It's not really the pressure, that's just timing.

It depends on the beans and roast; your comparison point is the first few (after pre-infusion) drips that came out. The last ones are always going to be weaker and quite possibly more acidic because the puck is both drained and saturated at the same time. It's drained of oils and flavors, and saturated with hot water. 

Whether or not you can actually detect that difference should it be added to the rest of the shot is a matter of uncertainty, hinging on your sense of taste and the type of coffee used. If it's a dark-roasted robusta blend then you might be able to detect a slight almost 'metallic' or slightly salty flavor, but you'd need an extremely acute sense of taste. The water you use also has a lot to do with this.

It can sometimes be easy to get caught up in what is probably happening, even if you (or most) can't really taste it. If you get more satisfaction out of your coffee because you've managed to improve the taste even just a tiny bit - then great, and keep doing it, because that's what it's all about. Just be critical and test for yourself, with your setup, and your beans :)