I've watched enough bad Star Trek over the years to not be bothered by Time Travel logic. This one was no more egregious than your average episode of Voyager on that front, so I was able to just go with it.
My only real quibble was Captain America "retiring" -- the world is still in shambles (can you imagine the impact of 3-4 billion people suddenly re-emerging into existence? How many husbands/wives re-emerged into a world where their spouses had moved on without them? Or the number of religious cults that probably emerged around rapture suddenly finding everyone back?), and he decides to just piss off to the past and live out his own little fantasy of life with Agent Carter? I don't buy it from the character that he would ever be able to just walk away like that -- and that's before you even consider the weight Stark's death would have on him, knowing he talked him out of retirement and now Kid Stark is without her dad.
Captain America has been the strongest written of all of the MCU characters -- the ending here did a complete disservice to his character.