If I remember the episode right, some of the clues were only uncovered when the crew actively started digging.
Exactly. The point behind the episode isn't that they need to erase all evidence of their encounter. The point is, as Picard explained, Humans find a mystery irresistible
They don't have to eliminate everything, just enough to prevent their curiosity from spurring an investigation. It all started with Riker finding Data's behavior odd, at the beginning, followed by Crusher's plants (Which were likely replaced, ultimately)
If Crusher never notices anything odd about those plants, then she never reports anything at daily briefings, or starts looking into medical records, & transporter traces. No one becomes suspicious of Data. Crusher won't find out about Worf's wrist, even if there is evidence that it was broken, because even assuming it still hurts a bit, Worf isn't going to bring it up, unless ordered to report irregularities. He's a Klingon.
No one will be looking into the internal chronometers with a fine tooth comb. So it will likely never be noticed. It is even likely that they were more vigorous in covering up those clues, which would further decrease the probability of anyone, noticing them.
It's all about decreasing probability. Worf might get a pain inhibiting treatment. They might pick a better image for the fake world that got uncovered, in case it gets brought up. The only real concern is Troi's psychotic episode. Hopefully, the Aliens were able to do something to better wipe her memory so she doesn't get freaked by looking in the mirror
The principle of the story is "Curiosity killed the cat" or "Ignorance is bliss" or something. I really like the episode, it's very engaging, & the acting is stellar. Picard may have just been being melodramatic, to intimidate Data, with the "Stripped down to your wires" bit. He was trying anything he could, to get at what Data was hiding