TL/DR version. Don't be a jerk and it's unlikely anything will ever be notated about you, that you have not specifically requested.

The only thing that really stays with you is your skymiles account. Phone reps I know have the ability to put a note or two on your skymiles account...I do not know if the Airport people can see that or not.

We can also document PNR's which is 99% of what you ever hear about. The gate I know can see/add to that.

However...there are a few things to know.
A: unless you give someone a reason to start digging into you they are never going to look at the documentation in your skymiles account, or even document it in the first place. The only times I documented a skymiles account is when I suspected fraud. (Father and son using same account typically) Or when some became very abusive to me over the phone. And I worked in politics, what constituted as very abusive would make Bikers start to cry.

B: PNR's get documented all the time. It is important to note that the documentation only appears if someone pulls up your record...there is no note for the GA that I can leave that they will get without you talking to them.
Documentation happens mostly for 2 reasons: A note was adding asking for a special request that the current person you're working with can't fullfil.
Example: You tell me something happened and can't make your flight and I tel you that I can waive the change fee. But you don't know whe. You can go. I leave a note and the next person sees it and typically honors that.
B: You did something dumb. Like demanding something you are not entitled to, and being a jerk about it. If you're asking for an exception, ask politely and if you don't get the answer you want, politely hang up. If you make a huge stink they are likely to document the record as no one likes to be over-ruled when they know you are going to HUCA. Or you did something really dumb at the airport. If you get the GA documenting your record for the most part you've really done something stupid...full on temper tantrums, absolutely wasted, I saw someone who threw their briefcase at the monitor!