Herzog doesn't spend a ton of time thinking about his clothes. He'd much rather wonder about the nature of existence or of the meaning of life (or the ladeez). But he's 100% aware that his new flame Ramona "did not like his taste in shoes" (5.82).
There's something specific about shoes that Ramona cares about. Herzog wants to grow as a person, and he sees getting new shoes as the first step (heyo!) toward this goal. As the narrator says,
Strength, intelligence, feeling, opportunity had been wasted on him. What he could not see, however, was that such Spanish shoes—which, by the way, greatly appealed to his childish taste—would improve his character. And we must improve. Must! (5.85)
He may be a pretentious doofus, but he does want to change.
Now to be honest, it's silly for Herzog to think that buying new shoes will make him a better man. But who among us hasn't thought, in a moment of existential angst, "Wow. I could be the kind of person who could pull off a black turtleneck. If I got that black turtleneck I'd be so cool." Change often seems to be more possible when you obtain a new thing.
It's symbols like these shoes that make Herzog both a totally annoying character (C'mon dude, you're fifty. Shoes mean nothing.) and a totally relatable one (Oh yeah. I remember when I wanted those shoes/tablet/car/apartment for the exact same reasons).