1. Moore can't tell whether prices are going up or down. This is an important thing to know if you're on the Fed, half of whose dual mandate is stable prices.
Moore has repeatedly, and falsely, claimed that the country is experiencing "deflation." That means prices are falling, which they are not. But claiming this gives him cover to argue that the Fed should pump more stimulus into the economy just as Trump begins running for reelection.
Conversely, when we were in the depths of the financial crisis and prices were falling, Moore claimed we were on the brink of Weimar-style hyperinflation. He therefore called on the Fed to tighten monetary policy, which would have crippled the economy — and just coincidentally maimed President Barack Obama.
2. Relatedly, Moore claims official government economic statistics are phony when they don't suit his preferred political narrative.
3. Moore advocates — at least when politically convenient — crank economic ideas, including returning to the gold standard. This idea is roundly rejected by actual economists and would result in much more price volatility.
When called on such nonsense, Moore has claimed he never said such things, even after being presented with video evidence.
4. He cheered the failure of Lehman Brothers, an event that (foreseeably) set off a worldwide financial panic and nearly plunged the entire global economy into another Great Depression. This doesn't inspire confidence in Moore's instincts next time the Fed has to handle a financial crisis.
5. Moore lies, and lies, and lies.
About his own record, and about easily Google-able facts. Now I realize the word "lie" implies knowing intent to mislead, as opposed to possibly ingenuous misstatement of fact. But note that, even after being corrected on his various falsehoods — including about the Volcker Rule, Canadian tariff rates, whether tax cuts have paid for themselves — he has often repeated the exact same falsehood.
So either he's deliberately misinforming the public, or he's like the goldfish who forgets everything immediately after swimming a lap around the bowl.
6. More broadly, Moore prioritizes what's good for his party above what's good for the economy. Which is toxic to an institution that must be politically independent in both practice and perception to function.
You can see this tendency of Moore's in his monetary policy flip-flops, as well as his calls for Trump to fire everyone at the Fed who doesn't do Trump's bidding. Most recently, you can see it in Moore's explanation of the one concern that could persuade him to withdraw his Fed candidacy: if he concluded that sticking around might hurt the GOP.