I don't know how to reproduce these, but:
I have a situation where two subs are very close to arriving at an output at the same time sometimes get transposed in the time machine future. I don't know what causes it, but every time I have been able to back out to the game list and then reenter the game to fix it. (It's a big deal because one of the incoming subs has a specialist that only takes affect on subs and has a waypoint queued to intercept the other sub.)
I also had another situation where I launched a sub, moved the time machine forward to see what would happen, then went back and cancelled the launch, which caused it to disappear from the main screen but not from my time machine speculative future. After backing out to the game list and then reentering I could see the pending launch again, as though I hadn't cancelled it. I was able to properly cancel it that time, though.
Also—not a time machine bug, but still interesting—there's a case in this game with a launched sub that is going to fight with an output that still has drillers from an eliminated player. The sub has a blinking red warning light, even though it will win—as though the sub "thinks" that the destination outpost will be gaining shield or producing drillers even though it is dormant.
(And not related to time travel at all: another player's specialist hire has been blinking with "Hire becomes permanent in -3 minutes" for a very long time, definitely longer than 10 minutes.)