The thing to know about him is he was president for a month and then he died. That was his impact. He died. He didn't noticeably improve or worsen things (Based on his inaugural speech he might've been bad but he never got to act on it) because he had no time to because he died. Which consequently means he should be the null point we can base every other president on.
If the country was left even slightly better then you got it? Then you did a better job then Harrison. Was it left worse? Then you did worse. Did 40 presidents all make the country better and only 4 leave it worse? Tough to believe.
The guy gave the longest inauguration speech ever and did it in poor weather while not wearing the proper clothing. That directly contributed to his dieing a month later. His ego essentially caused his downfall, it's fair to rate him below the middle.
I think this is actually a common misconception about the presidency of WHH. He gave the longest speech, he (iirc) the oldest president at the time of his inauguration and that inaugural speech was ridiculously wrong, but there's no actual evidence to say it's what ultimately led to his death.
I could be wrong, but I believe that Harrison's death, and the death of Taylor a few years later are to some extent linked; the water was bad.
It might not have been the sole cause, but being in a state of hypothermia for a prolonged period will absolutely weaken you and make you more susceptible to other issues.
That's the thing according to the evidence we do have, he wasn't showing any signs of illness in the run up to very noticeable falling ill about three weeks after entering the white house. Not saying that it wasn't hyperthermia, just that it's very unlikely to have been brought on by his actions during the inauguration.