I think this is not a duplicate of the question John mentions. That question asks specifically why the balloon makes a spiraling movement, which in general is not the case (the answers pay only attention to two variables: the nozzle and air resistance, for which there isn't a fixed centre of drag) while I ask the broader question which variables make the movement chaotic (which it is for sure while its velocity responds in a non-linear way to these variables). The non-spiraling movement can be seen as a sequence of (infinite) little pieces of circular trajectories because there are other variables influencing the motion of the balloon too (like the chaotic air movement around the moving balloon, which causes a non-fixed center of drag).
When a balloon goes flat it makes a chaotic movement through the air. Is it the interaction with the air, the behavior of the part through which the air escapes (in which case the balloon will also trace out a chaotic trajectory on the moon), or what?