Plot hole: After running from the pirates, the two castaways almost stumble off a cliff. Unless they were running backwards, I'm sure they would have seen the cliff coming for a while, because when the camera zooms out you can see clear terrain for at least 20 metres until the edge of the cliff.
Plot hole: Alain joins the Legion, goes through extensive training and eventually gets his photograph taken. That's how Galgani recognises him and sends two men to kill him. They arrive with a platoon at the fort just after Alain, Mackintosh and Luther. The photograph would have taken a while to get back to France and then the two men would have to go through the same training. So how do they both end up in the same fortress after they joined the legion long after Alain?
Plot hole: When Tarzan comes to the hotel to visit Jane, he overhears the bad guys threatening the hotel clerk into giving them Jane's room number. Tarzan then has time to go into the streets and study the hotel for a little while (coincidentally just when Jane happens to appear in her window), climb to the second story and through her window, have a romantic reunion with Jane and explain what is going on before the villains have managed to ascend the one stair from the lobby.
Plot hole: After Riker takes the Enterprise through the Briar Patch to communicate with Starfleet he returns to rescue Picard from the collector in mere minutes, even though it was supposed to be a 2-day journey.
Plot hole: Considering that this family has been training for the mission for years and certainly have received some instruction in astrobiology, they are awfully carefree around the cute little alien. Any real space farer would be aware of the enormous potential problems with first contact, like incompatible biochemistry (aliens might exude deadly toxins from their skin, be eaten alive by human-exhaled oxygen, etc). They even feed it human food without analyzing the alien; again, this could kill it, make it chemically dependent, cause it to go into a mating cycle, etc. But it's cute alien, so naturally they don't worry about any of this.
Plot hole: Throughout the movie, Bladebeak works for the villains. But, during the climax, he becomes a good guy without any explanation.