Q was a nice plot device, and he was well used. An omnipotent being has no need for power games for he has any power he wants. What I especially liked was that they didn't try to make him a "god", i.e. someone craving worship, because anyone who had total power has no need for petty crap like that. He was quite believable. What would ultimate power eventually lead to? Boredom. That's exactly what happened with Q, and the Continuum. They were essentially incredibly bored. Bored enough that the exploits of an insignificant species become interesting enough to observe because they behave in an odd way, and bored enough that another one of them wishes to die.
It is likely that this is pretty much how an inquisitive mind reacts to total knowledge, total power and eternal life. It sure gets boring really quickly.
Wesley was ... well, a mistake, yes he was. He was the proverbial Mary Sue character. I think it was even revealed at one point that Roddenberry wanted to see himself in him, which makes him even more Mary Sue. It is kinda telling that the character was eliminated from the show around the same time Roddenberry died. In the end, the character was just not really believable, that was his fatal flaw. The youngest ensign in the fleet saving the day on the flag ship time and again... c'mon, it gets old. And again, it was the character, not the actor. Where Kirk was sometimes cringeworthy because Shatner is a crappy actor, Wheaton had little chance to make this character believable. When you're handed shit, you can only polish it so much. And in the end you sit there with dirty hands.
Borg children... never seen the episode. But we're (probably?) talking about an episode, there have been a lot of episodes that were rather... questionable in their logic. In TOS, TNG, VOY, DS9... and even more in Enterprise once the time travel sets in.
Piccard's style of operation was a cooperative one. There's not really a problem with that, and I don't remember a case where a spot decision was necessary and he instead went into a meeting. Kirk was a cowboy, Piccard a diplomat. Both of them due to the nature of the show they headed. Kirk was supposed to be a hands on guy, tough guy in a wild west universe. Not only 'cause TOS was basically a western show in disguise. Times change, and so do viewer expectations. The 90s were a decade when we believed we can solve all problems in the world by talking about them. That also explains the counselor.
Better and worse... all the Star Trek shows have their strong and weak sides.