There is no company so perfect to work at that you couldn't find a downside. Con Edison is no different.
Like any job, you've got a very diverse workforce and the range of personalities that come along with that. You better know how to deal with that or you're going to have problems.
There are a lot of people out there who lack good communication skills. Con Edison prides itself in supporting what they call their "core values" and "open communication" is one of them. I would prefer they change it to "good communication" or something that reflects more than simply being "open" because there are many people in both union and management that could substantially benefit from better communication skills.
Regarding recognition and feedback.... I wish it were better, but it's not. Look to get feedback from your peers, because in my position I spend a lot of time working independently. I would say that your own good communication skills might help to gain proper recognition and feedback. Other positions in the department work more closely with supervision so it is likely different than my experience. Recognition is rare, so take pride in the work you do because you know you're doing a good job. Again, there are ways to promote being positively recognized so a good effort in this area will bring it's rewards.
Senior management... If we're talking about the CEO and top-tier management - who am I to judge them? I don't work with them, I likely don't understand all of the complexities of the issues they deal with... The company is profiting, we all still have our jobs, life is good - so I give the top-tier management an A+ for their work. Mid and lower level management... Good people - all of them. I don't think I've met anyone who didn't take their job seriously. But there is an adversarial relationship that is clearly evident between union and management that interferes with the way things get done. That doesn't necessary put all the blame with management, though. The bottom line is that people who understand how to act professionally manage to get things done with other people who understand how to act professionally.
In a perfect world everyone respects you and everything is handled fairly. Sometimes I'm really satisfied with things like fairness and respect and some days I feel like I don't get the respect or am treated as fairly as others. That's life, what else can I say. You can't be thin-skinned about these things or it will really bother you. But that's at any job and Con Ed is no different. It's a great job.