I haven't been around scouting too long, but long enough to hold every position on the committee (in the same year!) and to be a Tiger Den leader and Webelos den leader, so learning on the fast track!
From what I have heard around the scouting world, it is wrong to hold back awards- at any level- in order for other boys to catch up. There will be scouts who never do the necessary requirements. Does that mean that nobody can every advance?? If a boy deserves an award, he should get it at the next pack meeting he attends. It is true that Webelos den leaders need to sign off on requirements, but I feel that the requirements can still be done at home as long as there is proof. I ask my Webelos to bring in documentation. Just about everything for the Webelos badges can be documented. There are several badges- Family Member, Traveler, Handyman, and Scholar- which can be done at home if the den leader agrees. Also, several of the Webelos badge requirements (like the parent reading the Webelos book info and the religious portion) are often done outside of the den. When my son did badge work at home he documented what he did. I also believe that doing activity badges should not entirely at the whim of the Webelos den leader. If the boy has interest in something in particular, then he should not be held back from doing that badge at home. He may have to repeat the badge work if the den does it later, but he will just get more out of it. I am tired of parents being told by school and scouts that they must hold their child's interests back to go at the same rate as everyone else.
As far as the rules, it depends on which is being broken. I don't believe there is a place for free-for-all-in-the-name-of-fun chaos. Scouts is supposed to teach character, and this can be done and still have fun without scouts disregarding other people and property by being disruptive. But I don't go so far as to worry about tucked-in shirts. That's just me, because I think that the rank-and-file military aspect of scouts should be downplayed for boys.
Karate is not allowed by BSA. I wish it was- my boys do Karate and would like a belt loop for it.
What to do about boring and unqualified den leaders? That is a common tough question. If you cannot make it to the meetings yourself to help, then I would say try to line up outsiders to teach the Webelos activity badges. Tell the leader: hey, I found a great geologist/engineer/scientist/musician/etc who is willing to teach a badge. I would imagine the den leader would be happy to have someone else do the work! Our pack has one den leader who is great at finding resources: her Bear den has gone to a car sales lot, a hospital, a grocery store, the police station, the boat marina, etc. She says it is easiest to farm out the work, and the boys are really getting a lot out of it. Also, boys listen better when you bring in the "guest expert."