I honestly think it's one of the big lessons lost these days. Let them run their suck, but when it's time to get it on, put the hammer down hard and END it. Too much trying to soft shoe stuff. Once the time for talking is over... it's over. Ask, tell, make. Be decisive. If you have nothing, get stepping.
Coping skills. You will see the worst humanity has to offer, you will see and participate in extremely violent confrontations, and you will have thousands of hurts both big and small over your career. You may bury your friends. You may be the one to knock on the widow's door with the chaplain to break the news. You may see your best friend drug through the mud in the media, and next week it'll be you. You will see children who'd be better off raised by wolves. You will see the elderly discarded into a backroom, neglected, abused, and used for their SSI check and pills. You will be confronted by the chance to enact your own version of justice and will have to live with the choices you make, no matter which way you chose.
I don't know if it's a "skill set", but the ability to care without making it personal. You have to have pride in your work and the drive to do it, but not to make it personal between you and the shit bag. It's not "you vs him" and if you let it be you'll eventually fuck up or eat yourself up. It's you doing the best you can do and to accept that this is not going to result in an arrest or justice every time. There will be a next time. Getting pissed about what a victim does (recant, fail to show up for court, etc.) a prosecutor does (plea to some ridiculous bullshit despite the airtight case you handed them), and ESPECIALLY what a judge or jury does because you can't control it.
Keeping your dick in your pants doesn't seem like much of a skill, but the failure of doing so ruins a lot of careers and a lot of families.
Then just general life skills. Knowing how to manage your finances, balance work, family, and solo time, etc.
While I am far from an experienced LEO, there are two things I will take every opportunity that I can to improve: Communication and situational processing.
The overwhelming majority of my job related tasks requires communicating. From interviewing subjects/involved individuals and getting buy-in from my co-workers, to selling an operational plan or policy to my superiors, I use communication skills more than anything else in my toolbox. This extends to writing up affidavits and all the other memos and reports associated with investigations. Better writing leads to fewer headaches.
Situational Processing is hard. My hard skills are not noteworthy in any way, but in almost every situation the limiting factor is my ability to figure out what is happening and which response is most appropriate. Training that focuses on escalation of force, or live fire/simmunition scenarios are the most valuable skill development opportunities that I have had. I am a mid C ranked USPSA shooter, and I can easily out shoot my processing ability.
In a previous active duty life, physical fitness was huge, but the same things were what made someone stand out. Know how to shoot move and communicate. More specifically, know what to shoot, when/where to move, and how to communicate.
Forgot to add, every rookie we get I give a copy of Emotional Survival for LE. It is a good book, lots of good info.
VDMSR.com
Chief Developer for V Development Group
Everything I post I do so as a private individual who is not representing any company or organization.
And as to the OP, this.
I would add that don't forget that we should aspire to be "Peace Officers", not Law Enforcers.
The "book" doesn't always provide the best answers. Think outside the box. Be the kind of Officer that people you respect and love would want to respond if they called for help.
Tons of great advice here. I'll reinforce a couple of points:
1. Learn realistic expectations. You will NOT become Superman when you put on the badge. You CAN NOT save the entire world. You WILL lose sometimes, on the street, in the squad room, and in "real life" outside the job. When those truths hit home DO NOT self medicate. DO NOT bury your sorrows in the loving arms of someone who isn't your spouse/partner/steady whatever.
2. Learn patience and a calm response to stress. Responding with anger WILL NOT help, no matter how good it feels at the time. DO NOT confuse what I just said with meaning you have to be Mr. Nice Guy - hopefully your training and your FTO will teach you to recognize when you need to get on top of something right away, and you'll do so with every ounce of aggression in your being. I'm reminded of Gen Mattis' quote: "Be polite, be professional; but have a plan to kill every person you meet."
3. Learn to communicate. You need to be able to talk TO and WITH people, not AT them. You need to be able to write clearly and concisely - the better you document, the better your life will be. If I had a nickle for every time a co-worker did a rush job on documenting a contact that resulted in unnecessary Court time, I could have retired a long time ago.
Curiosity. A good cop always is always looking for the criminal. It's in his blood. He can't help but seek out the wrong in the world.
Compassion. I routinely choke up. I'm not weak. I simply hate seeing bad things happen to good people. Don't lose it. It's what makes us better than them.
Confidence. You have to have faith in yourself. That no matter the what, you're the who. You may not the strongest, fastest, or best shot but you'll still win the fight. Somehow, someway.
Everything else you can learn.