The film, in brief, involves a boy named Davey being picked up by a survey ship he calls Max, taken to Phalon, a star distant enough that he does not return for eight years despite traveling at speeds exceeding the speed of light and experiencing almost no time himself, and returned to a time and place where he has been a missing person expected to be considerably older than he is.  Meanwhile, the survey ship crashes, is captured by NASA, and loses part of its database, so it needs the backup copy it stored in the "unused" part of Davey's brain.  Then it is evident that Davey is not going to be able to live a normal life without returning to the time from which he was taken, so Max takes him back and releases him not far from where he was acquired.  Sure, there are several problems there, and we address them in our analysis, but the time travel issues are our main focus.

The problem, as we saw it, is that the Davey who arrived in the future (1988) had been missing for most of a decade (since 1976), but that the temporal duplicate Max has now taken the duplicate Davey to Phalon and will return him in 1988--but that when that Davey returns home, the older version of himself will already be there, not having been missing at all; and the duplicate Max will also be captured by NASA and need to be rescued.  We thus have a very complicated time travel problem.  Our resolution, in a nutshell, involves the older Davey and his brother working with the younger Davey to free Max and send the younger Davey back to 1976; it also involves a sawtooth snap, because the experience of the younger Davey is different from that of his older counterpart, so he has different memories and is a different person, and we have to play the game again to get it right.

Eugene suggests a shortcut to this, based on the known abilities of Max.  Max has the ability to travel in time; he also has the ability to plant information in human brains.  In theory, he could return Davey to 1976 and then rendezvous with himself, and upload to himself a datafile with all the needed information to avoid the events of the movie and cause Davey to remember them as if they happened.  The duplicate Max would then know that he had to install the file (so he will be identical to his future counterpart) and write memories in Davey's brain before returning him directly to 1976, avoiding the NASA entanglement entirely.

As Eugene suggests, this would make a much less interesting movie, but it is a much neater solution to the temporal problems of the film.  Because Max is ultimately an intelligent machine, he probably has the capacity (as we noted recently in looking at Free Birds) of programming himself to be identical in every way.  Kudos for a clever solution, and thanks for reading.