How do you deal with mediocre superiors and their lack of leadership?

I manage my "four walls" and take care of my formation while shielding them from as much as I can. Hopefully it rubs off on those appointed over me.

Have a good idea and make it look like it was theirs. Timing is everything

When I was in, I had just been academically dropped from the Nuke program, and force converted from Electronics Technician to Data Systems Technician, and sent to a 'C' School for the AN/UYQ-21 Combat Display Systems. After graduating from the 'C' School, I was giving orders to the USS Carl Vinson. When I first got there, command was happy with me and talking me up and at first talking about how they were going to give me great evals for the upcoming test etc etc. Then as the time approached, they decided all of a sudden, they had too many E-5 already and didn't want another E-5 in the department (I was an E-4). So, of course I was a tad pissed, after they just spent the last 3 months blowing smoke up my ass. Well then, they had the "Command Retention Team" going around department to department trying to get NCOs and above to reenlist etc.
They CRT team really wasn't happy when I told the Senior Chief "you must be out of your fucking gord if you think I am going to re-enlist, after y'all pretty much lied to me". But then he had to admit, he would be a bit salty too.

Take charge

I raise my level of performance where possible so that mediocre leadership is not evident

Unfortunately you will run into this throughout your career. My way of dealing with this was always show respect and avoid interacting with this type of leader as much as possible. Granted avoidance is not always possible but treat each interaction as a learning experience for yourself and push your lack of confidence of the superior to a far back burner. The biggest mistake you can make is to let your lack of respect show, thare is almost no way to recover from that when you are dealing with a mediocre superior. As others have said, one of you will move on, so suck it up and take the high road.

Make them feel like the heroes they mistakenly believe they are so they don't ruin your career.
Zero career points for pointing out what is obvious to everyone but them.

Let him know anonymously that he is going to get fragged during the next firefight unless he corrects himself.

The only mediocre leader we had was a Gs10... wasn’t worth a hill of beans. I be wotking with the cooks assigned me and getting production done showing them how to put more professionalism into their product.. he’d come along say I was wasting his money showing them ‘that stuff’. He was getting me to the point of doing s’thing Zi didn’t want to do... “Mr. L,
I ask you kindly to vacate my AO so I can instruct these young Airmen to be more
Professional in preparing their product., Please!”.. at that he purposely knocked the pan of garnishes on the floor.. I looked at him and looked at the mess he had made. I knew the NCOD upstairs and called him from the office.. then I went back to the kitchen snd suggested he take some more cough syrup, he was sounding hoarse.
(He drank that stuff like water and it was loaded with Codiene). A few minutes later the NCOD came down(it was the weekend). He smelled that guy’s breath and asked him to go upstairs with him..
he resisted at first and the TSG called up to the Operator to call Security Police he had an inebriated person in the kitchen ..
we had a small crew of Sec. Police assigned to the Hospital and they were ther in a matter of about 5 minutes. Later at his board hearing he insinuated I entrapped him. I stated that he should take some not drink half the bottle.. he put himself in the precarious sitrep.. They would have suspended him two months or check into mental health for alcoholism. (Which was 3 months but it go on his record as a medical leave). When he got off I was enroute to my new base in ND.
I had 6 days travel, 30 days leave. I used 3-1/2 To 4 days travel and no leave... that guy didn’t give up.. he said I cheated them out of 15 days work .. AF said I can use my leave or not use it.. I was a couple days into travel when I decided to get to base and sign in and save the leave. I had just had some leave in May.. The Civ. Said he was drawing up charges and I’d have to go back out and answer to them..
Grand Forks said; “don’t worry, you’re mission essential personnel here. We got you covered SSG. No civilian feather merchant is going to “F” with our aF Personnel . You belong to SAC, Now!
Now, that is what I call supportive.. All they knew is about the leave sitrep and that’s all they needed to know. Before I Left, The CMSG endorsed me a 8s and 9s
APR which was top of the line and forwarded Personnel a copy and gave me a copy and sent one ahead to my gaining Unit. I got a phone call from a friend in my Section and he was livid.. said he claimed that CSG had no Authority to endorse that like that(when in fact he did).
I had good faith that my Comrade was being truthful. I had my CMSG Super check to see if any amendment could be made. He assured me that it wojldn’t Matter, I’d been in the Command too long at that point(9 mo.).. excuse me for saying;.. I think that civ gs10 had a “hard-on” for rectifying what he thinks I put him through.. along with the leave sit-rep..