Yeah, I know. Now that I'm gone, I bet everything is amazing. I'm not even joining the servers for fear of screwing things up because I just know everything is A-Okay now.
If only I knew that leaving was the only thing needed to make the server great again!
The word you are looking for is omniscient.
It's nothing to do with admins but rather with tools that are given according to rank, the tools are what matters.
There's an attack log for the entire server that logs every attack you make on another player (and this includes hitting them with thrown objects which also includes bullets).
During a round, an Admin can also see in your vars a log for the current round showing who attacked you and who you attacked, by chronological order.
This is why the "he attacked me first!" shit doesn't fly.
There's also a log for explosions. Pretty much every simple thing with ex_act has a line to log itself, it's coordinates and who did it in that log. For reference, whenever a player makes a bomb and detonates it with a remote detonator, the log says who held the bomb last, who used the detonator, who made the bomb, who made the assembly, the location of the bomb, it's sizes and time.
This is why Tzentch story about "I swear, I lost my 7th bomb in a row and for the 7th time, someone completely at random found it in a locker in maintenance and knew the code!" didn't fly either.
There's also a log for other miscellaneous shit. You mess with the PA, it logs your account and what you did with it. You shutdown power in Engineering to release the singularity, you're logged too. There's a few other miscellaneous crap as well, generally for wide destruction too, like welder bombs.
Keep in mind however that all of these measures were implemented because someone abused them hard enough to actually become a problem for everyone else. They came out of necessity, not just carebear attitude. If you do something that's not on that list and actually become a problem, expect a "fix" soon.
Goons for instance made some very specific chemical mixes log you as well (and explode on your face) because of shit chemists, for instance.
This is also why I often urge people to not abuse exploits. We could still have the crusher infinite ore bug if there wasn't a cunt that, for several rounds in a row, kept making uranium floors and diamond walls just to prove he could.