I think if anything, they should make LESS mistakes.
How often do we have to see referees (and wrestlers for that matter) seeing someone not involved in the match and being totally "distracted" for a good enough amount of time that they're not even really doing their job and they allow someone else to win?
If you want to talk about realism, why is that so overlooked when its completely unrealistic? Every single Finlay match, Hornswoggle comes out, distracts the ref, and then Finlay can hit the guy over the head with the shillelagh and get the win. It happens EVERY SINGLE TIME. You'd think by now the referees would know about it because they'd be watching the replays and shit that we have to see 40x a week. So if this was realistic, they'd see Hornswoggle and they'd either ban him from ringside or the second he started distracting them, they'd know he was doing it to help Finlay win the match illegally and by default, they'd disqualify Finlay. You can't keep your managers and valets from interfering? Well, tough tits, that means a DQ, cause they shouldn't be a distraction.
The referees not being told the end of the match is good for some things and bad for some other things. It helps prevent the ref from looking like he knows exactly what's coming next - like when his hand doesn't even come close to hitting the three because he knows its not ending then - but at the same time, it leads to mistakes that break kayfabe. When Morrison was pinned on ECW from a Side Effect off the top ropes that Matt Hardy did, the ref counted to 3 when he was supposed to count to 2 and be interrupted by the Miz. Something went wrong there and Morrison saw that Miz wasn't showing up, so he had to kick out himself, but the ref counted to 3 and the match ended prematurely. After that, we saw that Morrison was perfectly fine, everyone was confused, the ref looked scared shitless, and Mark Henry had to save the day by attacking everyone as a means to get the crowd to not pay attention to the flub that just happened lol. That ref was soon future endeavored.
If you wanted to go for more realistic, the playback feature should be used more often to restart matches and 86 the pinfalls and such. But that wouldn't allow the heels to cheat as often as they do (although that, to me, cheapens the wrestlers a bit too when they can NEVER win a match without cheating...but that's another discussion altogether).
I wouldn't mind seeing some differentiated "planned mistakes" to replace the same old "Hey! You're not supposed to be talking to me! You're not the legal man! Why are you distracting me?! I'm just trying to do my job! Whoops, suddenly his partner is getting the win! Better go count it!"