Plot hole: How do they maintain communication between the ship at the centre of the earth and the surface? There's no wire, and radio waves can only travel any distance without obstacles, and the earth's crust would be a pretty hefty obstacle...
Plot hole: The Toymaker throws that toy bird at the hippie version of himself. The toy goes through him because he is a hologram. Later, he pushes the soldier version of himself at the screen making it crack. How could he if the three others are holograms?
Plot hole: When the Drakes (Bobby's family) arrive home they are acting quite naturally, until they find Wolverine there and get a start. Later on we see that they had parked their van in the driveway right behind Cyclops' car, which Logan and company had borrowed and parked there. Wouldn't they, seeing a strange car in their driveway, be suspicious or at least enter their house asking "Bobby, are you home?" (00:52:45 - 00:59:15)
Plot hole: Throughout the film, anybody who speaks English uses Modern English, with either a British or French accent as appropriate. However, 1357 was solidly in the Middle English period. Although that language would not be utterly incomprehensible to modern-day travellers, neither would it be indistinguishable as it was in the film. The film specifically draws the viewer's attention to language at several points, making suspension of disbelief impossible. The French speak French, and very few of them speak English. There is a scene in which Andre is talking to Claire, and her lack of knowledge of modern idioms makes the conversation difficult; that should be true for all characters at all times. If the historical people were talking alone among themselves, I could accept that they're being "translated" for us. But they're talking directly to the modern travellers - it's too jarring.
Plot hole: When the team plays back the record, it contains an extremely high-pitched tone which triggers the crystal sensors on the ship. But the speech on the record is low quality. This low quality would be the result of extreme frequencies being lost; but if they were, the trigger tone (a VERY extreme frequency) would be lost too. If the League's gramophones are capable of recording and playing such a tone, they should also be able to record and play back the speech without any quality loss. (01:09:05)
Plot hole: Just before Cowboy finally opens the bowling bag, the zipper is halfway up the right side. John was warned not to open the bag and was terrified by the potential consequences; he didn't open the bag at any point and certainly wouldn't have allowed it to remain partially open. (01:13:30)
Suggested correction: This isn't a plot hole. It's just your unfounded assumption. There's no evidence to support the supposition that the T-X has such audio detection capability.
Even if she could detect it, how could she discriminate between the sound of Catherine breathing and that of the dozens of caged animals in the room? That's stretching even fictional technology a little far.