Cohen, when asked to name the greatest things in life, includes "good dentistry", indicating that there are dentists in Discworld, yet, when he finally has dentures made, he has them made by a jeweler out of trolls' teeth.
Cohen's teeth can be seen in several shots before he gets his dentures.
When Cohen first sheathes his sword (around the 18:30 mark), he completely misses his scabbard, yet the sheathing sound is heard.