Ok I have at least part of the answer here.
Situation: You have one ship left to move manually, having N movement points remaining. There is a target that you wish to attack, N+1 squares away. Moving manually you cannot normally hit it, but if you autopilot-attack it, (right-click on that target to autopilot the ship to it), then you can hit it. If you do so as your last move of the turn, your autopilot ships will not get their cue to move, (this includes your civilian trade freighters), before your turn ends.
This bug may also arise in other situations as well, not just autopilot-attacks. (Possibly any situation that involves you invoking an autopilot move as your last move of a turn.)
Workaround: First, you must have the Auto Turn option turned OFF. After your autopilot-attack, move any ship out of orbit and immediately move it right back into orbit. Your autopilot ships will then get the cue to move, (including your civilian trade freighters). Now you can click the Turn button manually.