As with everything else, Harpagon takes nearly every opportunity he can to save money on clothing. When a servant complains to him that his clothing is torn in the back, Harpagon merely answers, "Stand so you keep your back to the wall and face the company at all times" (3.1.9).
Here we have Harpagon's cheapness and insecurity blending together. Harpagon's #1 love is money, to be sure, but he's also pretty obsessed with how people perceive him. He wants to give a good impression. But because he has the emotional IQ of a sea slug, he doesn't put it together that the easiest way to make a good impression is to look sharp, and to have your servants look equally snazzy.
Harpagon's son Cléante does have a good-sized sense of social presentation, and he dresses to the nines. But Harpagon is blind to the fact that this is 17th century France and dressing up is a high priority. Seriously, check out the duds in that engraving. Serious business. The motto of 17th century France might very well have been 'Look Good, Feel Great.'
Harpagon is worried that when his son wears nice clothing, it will be evident to all of Paris that he is a wealthy man and that people will come and rob the house. His love of hoarding dollars keeps him from attaining his precious goal of getting respect.
Harpagon thinks Cléante is a flake because the kid spends money on clothing when he could be making lucrative investments: "I'm willing to bet that your wigs and ribbons cost you at least twenty pistols, and twenty pistols, even if you got eight per cent, would bring a return of eighteen livres, six sous and eight deniers per annum" (1.4.37). The fact that Harpagon reduces everything in life to dollars and cents helps to show not only that he's a miser, but also that he's so money-obsessed that he's blinded to social realities. He's not respected, and he's not respected because he's such a skinflint.