I don't really understand the original objection. The crew "didn't trust Data"? They did - they did not throw him in the brig or hold him at gunpoint. They weren't suspicious of him, despite Tasha Yar asking a few sensible questions. Riker just sent Wesley to keep Data company because he was behaving slightly oddly and might have been in need of some benign companionship. Riker wouldn't have sent in a kid who didn't have backup and who didn't even report back immediately (nor apparently was expected to) if he truly suspected Data of evildoing.
And the resident android (that is, the weekly willain imitating him) only truly starts acting in a suspicious manner when the Crystalline Entity reappears anyway. It's at that point that Picard suddenly refuses to believe Data is in fact Lore in disguise, against all evidence - but that's hardly evidence that Picard would be stupid. Rather, despite claiming he doesn't believe Wesley's accusations, he immediately acts upon them, putting Lore-playing-Data under covert surveillance by an armed guard. Apparently, he was merely playing along, trying to silence the stupid kid who was blurting out the truth and thus almost alerting Lore.
No, the crew isn't stupid or failing to react at that point yet. The point where stupidity enters the picture comes a bit later... When Lore puts his shield-dropping plan in motion, it's not Yar's armed guard that intervenes, but Data and Wesley and Beverly Crusher. Why? Where is the guard? How did Lore give them the slip?
Of course, it would not be unrealistic for him to be able to do so, after beating up Worf: he must have dozens of android tricks in his sleeve, and indeed could much more realistically be expected to pull this off than Dona Ragar in the later "The Hunted". Note that he does end up in a cargo bay that prominently lacks the tree he claimed he would be transporting, so he probably isn't where our heroes expect him to be.
No, Lore shedding his armed overcoat is not a plot hole as such. The idea that Data and the Crushers would find Lore faster than the security force does is... And the idea that they would confront Lore when finding him is example of utter character stupidity. Or more exactly, Wesley is being stupid when he offers himself as hostage (but he's a stupid kid and should be excused), and his mother is stupid in allowing this to happen (and she doesn't have an excuse).
The rest of the episode's plot problems relate to the inability of the Tripoli to unravel the mystery those decades ago, or of Starfleet to have done so between that time and the present. But those problems are easily shrugged off, argued to represent realism where the hero organization cannot really spend the time and effort on such things in the vast universe it is expected to explore and patrol.
(Also, in retrospect, Lore should not have had control of the ship's shields when he started toying with the cargo transporter. He would already be known to be on a mission of evil - and indeed nothing in the episode indicates he would have been able to drop the shields. If he managed to do that, the Crystalline Entity ought to have attacked at once, yet it didn't. It's only later on, in "Brothers", that we learn Lore somehow survived his beam-out, which might suggest that the shields really were dropped. Unless, of course, he was beamed into a point within the shield envelope and not through the shields, but in that case our heroes were remiss in their duties in not spotting the surviving Lore.)
BTW, does anybody else think that Lore was delusional when thinking he could converse with the Crystalline Entity? There's no indication in this episode that the Entity understood what Lore was saying. And indeed "Brothers" raises the possibility that Lore managed to drop the shields yet the Entity failed to follow Lore's plan, suggesting there was no true communication between the two.
Timo Saloniemi