Making the wrong call on Martinez, renewing Aubameyang and retaining Xhaka, are three decisions that I think call into question Arteta's potential as an elite manager, that's if you make allowances for the struggles we've had on the pitch (which I do).
We as fans can have our opinions and hindsight is a wonderful thing, but Arteta was there in training, he knew where Martinez was at in terms of confidence and readiness, and he simply made the wrong call. No ifs or buts, he fucked up. A very costly mistake.
And it's the same with Auba. He's not the right fit for the football Arteta wants to play. He can't play up front in the way Arteta wants him to, and he's a very limited dribbler when shunted out wide. Arteta knew the direction he wanted to take the team in the season after he counter-attacked his way to the FA Cup, and he must have known Auba wouldn't thrive in that set-up (even if no one could have predicted how low Auba has sunk). He should have let him go. The fans would have gone crazy, other fans and pundits would have ridiculed the club, but he would have been proven right, if he had taken the money and invested in quality players that fit exactly with the way he wanted to set up the team. Similar to Guardiola ousting Ronaldinho and Eto'o in his first year at Barcelona.
And Arteta's done it again with Xhaka. Okay, so we didn't sell a pretty decent player for a packet of crisps to a low-balling Mourinho, but now we have a guy that is as leaden footed in body as he is in mind when it comes to seeing an incisive pass, who at the same time is also by far the biggest personality in the squad - it's play him or suffer big disruption in my opinion.
All of this is not to say Arteta isn't a good coach, and can't go on to become a very good one - Guardiola is a genius, and I rarely ever use that word, nobody else would have done what he did at Barcelona, so the comparison is wildly unfair - but, Arteta has made some very big errors already that have cost us badly. I have no doubt at all that if he could turn back the clock he would immediately transfer list Bernd Leno and let Auba go for free, and I think the same will apply to his decision to keep Xhaka
A case can be made that the right decision was made at the time and in the circumstances, but the very best are one step ahead, 2 or 3 steps even. Hopefully he'll learn from it in the long-run and we see the benefit of that.