There are a few different places in which money, such as ducats, coins, or pounds, is used as a reference to create a comic effect.
The first place is when Maria quizzes Sir Toby about bringing Sir Andrew into the house to be a suitor to Olivia. Toby defends his position by arguing that Andrew is as "tall a man as any's in Illyria," which is apparently an attempt at making a case for Andrew's looks (I.iii.18). When Maria catches the weakness of his point, asking, "What's that to the purpose?," Toby reveals his real reason for inviting Andrew into the house as a suitor, saying, "Why, he has three thousand ducats a year," which is a comment on Andrew's salary, showing us that Toby really just wants to get his hands on Andrew's money (19-20). This revelation is comical in the sense that it is also ironic. It is ironic that Toby wants Andrew to court Olivia so that Toby can access Andrew's money. Normally a suitor's money would have nothing to do with his so-called friend; the money would belong to the suitor alone, and should he marry, he could choose to share it with the bride. Hence, the fact that Toby is trying to set Olivia up with Andrew so that Toby can access Andrew's money is both ironic and comical.
A second comical reference to money is when Viola as Cesario pays Feste for entertaining her with his plays on words. He next asks for a pair of coins so that they might breed, saying, "I would play Lord Pandarus of Phrygia, sir, to bring a Cressida to this Troilus," which is to say that he would act as a "go-between" to help pair a female coin with his male coin so they might breed, just as Pandarus of Troy acted as a "go-between" to join Troilus and Cressida together (III.i.49-50; Shakespeare-online, Twelfth Night). This is also comical because his idea about breeding coins to make more coins is, of course, ironic. Coins cannot breed together to make more coins.
A third place in which money is referred to in order to create a comical affect is in the final scene. Just after Sebastian hurts both Sirs Toby and Andrew, Andrew exclaims, "I had rather than forty pound I were at home," meaning he wishes he were home rather than having his last remaining forty pounds (V.i.185). The irony is that we know very well Sir Toby has been draining Andrew of his money, and if he had staid at home instead, he would not be down to his last remaining forty pounds. Hence, even this reference to money is comical due to its irony and is also revealing about the characters.