To the first question, it depended on who you asked. To the second, possibly a bit on fiscal responsibility, a bit more on the recognition of Israel, and some good jokes with bad ties.

A bit surprisingly, there's very little in the academic literature about the contemporary view of Truman's sartorial habits, but he's now pretty widely (albeit informally) viewed as one of the best ever Presidential clothes horses. He used the contacts left over from his days at the haberdashery as his personal tailors - especially Stephen Brod - and given he was very proud about maintaining his weight within roughly 5 pounds (edit: ok, probably closer to 10 even though Truman claimed otherwise; I missed the Vaughn letter to Brod about him 'gain(ing) approximately 8 pounds [over a couple months in the early fall of 1945] and seven of that eight is right smack in the middle' - ouch) over 40 years those tailors had little problem making sure what they produced fit him well. There are stories about him going through four or five shirts a day on the 1948 campaign trail so that he never looked anything but spiffy; compare that to Wendell Willkie in 1940 who despite getting a reputation as a rather dashing candidate also got one as someone permanently rumpled.

The Truman Historical site maintains a remarkable collection of Truman's suits (helped, no doubt, by the fact he tended to never really throw stuff out if he could avoid it - large quantities of things just wound up in trunks in Bess' attic), and both the digital collection and the commentary are worth noting. Apparently he did come under some criticism from fashion writers both foreign and domestic for being slightly slow to follow trends. I would note, however, that one reason he may have really enjoyed going back to double breasted suits during his administration was as a response to the pressure on men's fabric use during World War II, which made it somewhat unfashionable to wear them even if they were of pre-war manufacture. He appears to have been fond of the way that they looked on him, and it is very Truman-like that he simply told the Brits who criticized him post-war that it wasn't any of their business that he'd not moved on from them.

As far as policy, Ferrell extrapolates on the failure of the Truman & Jacobson haberdashery and the resulting struggles over the next decade; he argues all the stress of being a debtor changed him enough so it that directly led to the Truman Committee taking a very hard line with military contractors profiting during World War II. I'm not sure I fully agree with that; Truman had speculated a whole bunch prior to the haberdashery, but was never really a spendthrift personally. You can make just as good a case that since he really enjoyed lengthy drives it was just as much a part of how the Truman Committee came to be; some of the earliest ad hoc investigations came from him hearing tales about contractors wasting large amounts of taxpayer dollars and being the only member of Congress that was willing to hop in his car and drive several hundred miles to see if there was any truth behind this.

The Truman and Jacobson failure did follow him around on the campaign trail, largely because portions of it had been litigated and were in the public record, and a general epithet for those who didn't like him was 'that failed haberdasher in the White House.' Jacobson, who Truman had successfully gone into business with prior to the haberdashery (they'd run a canteen at their stateside military base and made some money), did get used as a backdoor gambit when Truman had finally lost it with the constant lobbying of him to recognize Israel. From Hamby:

"As Jacobson recalled it, Truman’s rage at Jewish leaders who had criticized and been disrespectful to him had left him “at that moment as close to being an anti-Semite as a man could possibly be.” Reminding his old friend that Weizmann [the soon-to-be first president of Israel] would be the last person in the world to insult him, Jacobson said, “It doesn’t sound like you, Harry, because I thought you could take this stuff they have been handing out to you.” Truman turned in his swivel chair, looked out at the White House rose garden for a minute, and then turned around again and replied, “You win, you bald-headed son-of-a-bitch. I will see him.”"

This was probably as close as anything came to his fashion affecting his leadership, since Jacobson did visit his old friend in the White House something like 30+ times during his presidency (including the relatively sacrosanct Presidential getaway of Key West), which was on the high side even for old friends from Missouri.

Last, Truman did enjoy terrible ties even if he had enough fashion sense not to wear them in public. When Bess abandoned Washington and took Margaret with her, one thing he wrote about was that he hated that he couldn't play one of his favorite games, intentionally coming out in the morning in an absolutely hideous tie to be met with loud objections from 'his girls' before he changed it. There's also a story from an end of year budget meeting in 1949 where he showed up with four dozen or so Christmas neckties hanging from an extended arm, telling his staff, “They’re pretty awful, but take your pick; the haberdasher’s back in business.”

Edit 2:

Vaguely remembered there was a display of his shoe collection online and found it; in partnership with the National Park Service, a private site put some work in and catalogued what turned out to be 97 different types of shoes, many custom made. His suits tended to be well tailored but not expensive (save for when one of his later tailors would make suits from his top of the line fabric but charge him at low end suit prices instead, never letting him in on the bargain he was getting) but his shoes were stylish as well as being sturdy enough to hold up for walking 5 miles a day for exercise at the 120 steps a minute military pace he kept up until very late in his life.

Edit 3:

And as it turns out, the Trials of Harry Truman biography released earlier this month which focuses on his administration does have a brief blurb about his style:

"The very idea of Harry Truman as the nation’s leader [at the beginning of 1946] was so off-putting to many of the city’s insiders that even his wardrobe became a target. Truman, it was said, dressed “like he had just come off of Main Street in Independence… everything was a little too precise.”

In other words, he stuck out precisely because he dressed as who he was: a middle class Midwesterner who had come up in the world. This was a change from either rich shabby (the choice of FDR and old money) or in the very fine fabrics of the silk stocking Wall Street/'striped pants' (his term for the diplomats) crowd, and fit with his rivals and enemies perception that he was in over his head.