Well, for onething, we wouldn't have had the famous "radio razzle dazzle" - Nazi spies tried to sneak around and see what could be found out about the Manhattan Project," and instread some smart guy decided to make them think the secret was improvements in transistors - of course they were working with radios and other items as one of the many projects the Americans had during WW2, but they gave the spies some experimental transistor radios - with no transistors in them! I would have loved to have seen their faces when they got back to Berlin.
(Of course, we kind of did when Hogan's Heroes did that episode that had the Heroes taking part in the caper, but still...)
I don't think the spies would have gotten anywhere near the Manhattan Project, but it was still good to have something else to give them.
But yeah, I wonder if they could have had the Mercury project without computers on board. I mean, there were computers to help with re-entry, and while having computers on the ground give instructions that would then be radioed up would, in theory, be doable, it seems pretty far-fetched. So, that may delay Project Mercury by several years.
(OOC: Not sure how early those "sandwich type" ones from above could have been done, but I'm guessing something about the early transistors speeds this up at least some; and, the Mercury capsule OTL didn't have computers, they really did use computations fromt he ground radioed up to the capsule.)