Expecting a time travel story to make sense is asking to be disappointed. The paradoxes are virtually impossible to resolve, so if you think too hard about the plot, you're almost certain to run up against nonsense. Better to just go with it, let the story take you where (and when) it will, and enjoy the ride.
That's my philosophy, anyway, so believe me when I say that my nagging dissatisfaction with the time travel in Men in Black III has nothing to do with anything so banal as logic. I don't expect the time travel to make much narrative sense; I do, however, expect emotional sense, some insight into how people think about the arcs of their lives, their regrets, their hopes, the paths taken or not. That's the underlying point of time travel storytelling. If you can't get that right, you just have a lot of cutesy riffs on history, real and alternate.
Men in Black III just has riffs, and those riffs aren't all that cute, at least not consistently so. Worse, the feints at an emotional payoff to the time travel go nowhere, deflating the whole enterprise. I wasn't expecting profundity, but a few solid emotional beats aren't too much to ask. Yet aside from the brilliant decision to cast Josh Brolin as a young Tommy Lee Jones, nothing about Men in Black III feels particularly inspired or sharp.