Very minor. The turbopump mechanism on the early Thor IRBM is not faulty. There are fewer launch failures.
In November 1958, America sends the first photographing satellite into orbit around the moon...
Result:
We win the Space Race in the first year. USAF in control of manned space shots. No man on the moon.
This seems unlikely to me. First, I don't think this is going to "win the space race". Both the US and USSR had a number of "firsts" early on (admittedly, the USSR had more of them), and the USSR will just shrug and do something else (like...say...launch a man into space; the Vostok program was certainly underway by late 1958, if only because it was closely related to their spy satellite program!). "Winning" the space race requires doing something that your opponent is incapable of matching with the resources he is willing to put forward; not necessarily landing a man on the Moon, but that's the best choice overall. Simply launching a tiny orbiter to the Moon (which would likely fail, given that no area of space technology was very reliable back then) hardly fits that criteria.
Second, whether or not it does the Air Force is not going to be in charge of all human spaceflight programs. NASA was already being formed by the time Pioneer 0 launched (the relevant legislation had been passed about a month earlier), and preliminaries of the Mercury program had already been started. Eisenhower was strongly against military dominance of the space program, and would not have allowed the Air Force to take leadership in that area. Assuming for the moment (incorrectly, I believe, based on the first paragraph) that the space race would actually have cooled down from this success, then there would actually be even less reason to allow the Air Force to lead US human spaceflight. After all, the urgency of the situation doesn't demand that Something Be Done Soon.
Now, it's possible that the Air Force does have a human spaceflight program in this timeline; greater US successes in space could easily tip the balance of the 1960 election, preventing McNamara from entering office. This, in turn, could very plausibly lead the X-20 program to see actual human flights by the late 1960s. But the Air Force wouldn't be the US space agency, by any means.
I've been thinking about a no-Space Race timeline (to follow ETS) for a while, and I think you need to have essentially a series of minor PoDs to actually avert it. Basically the USSR being a little less lucky and the US being a bit more.