It is early days and they are still undefeated, so some Arsenal fans might find it unfair that their team's title credentials are already being questioned.
But following a summer in which Arsene Wenger has already done some serious spending, the evidence is that the Gunners boss has not yet strengthened enough.
There are some positives: as with their last-gasp win over Crystal Palace last week, Saturday's fight-back from 2-0 down to draw against Everton was an indication that Arsenal now have the backbone they lacked when the going got tough last season.
But the fact they found themselves in so much trouble in the first place suggests some of their other old shortcomings have not been eradicated yet.
Defence: Struggling against power and pace
Wenger had vowed before kick-off at Goodison Park that his side would show they were not soft touches any more but they again found it difficult to cope when they faced a player with genuine physical power.
Everton's Romelu Lukaku destroyed the Gunners in April and they could not live with him this time either, despite claims from his manager Roberto Martinez after the game that he was not fully fit.
Lukaku again stayed wide right to target and torment Arsenal left-back Nacho Monreal, and all three of Everton's front players - the big Belgian, his compatriot Kevin Mirallas on the right and Steven Naismith in the centre - looked dangerous running at the visitors.
|Arsenal against the top sides|
|Since the start of 2013-14, Arsenal have conceded 22 goals in five away games at Man City, Liverpool, Chelsea & Everton. Last season, the Gunners lost all four of their away games against the teams who finished in the top five, including Everton, who beat them 3-0 in April.|
In mitigation, this was a makeshift Gunners defence - their first-choice centre-back pairing of Per Mertesacker and Laurent Koscielny are yet to play together this season, and Monreal is only playing because Kieran Gibbs is injured.
Calum Chambers, who has started the season at centre-back, is a promising prospect but he is still learning his trade, as has been seen this week.
Chambers almost cost Arsenal a goal in the first leg of their Champions League play-off against Besiktas, diving in to try to clear and letting Demba Ba in on goal. He did not get away with it when he repeated that error in the build-up to Everton's second goal, after Mertesacker had been muscled off the ball.
But Arsenal's lack of strength in depth in that department is their own fault. Wenger sold their usual back-up centre-back - and occasional left-back - Thomas Vermaelen to Barcelona the week before the season started, and he has not been replaced.
The Frenchman still has time to put that right before the transfer window shuts on 1 September, but the signs are he will choose to rely on the versatile but raw Chambers.
Filling in when and where he is needed will be great for the 19-year-old's development, but not so good for Arsenal if further mistakes prove as costly.
Midfield: Where is the enforcer?
Last season, Arsenal's problems at the back started further up the pitch.
There was little protection given to their back-line in the damaging defeats they suffered at the homes of their rivals in the top five, including Everton.
Worryingly for Wenger, the same was true on Saturday, when Mathieu Flamini was the only truly defensively minded man in their midfield.
In the first half, when the Toffees took the game to the Gunners, they found little resistance in that area, with their first goal a good example.
Gareth Barry was given time to pick out the perfect ball for the unmarked Seamus Coleman to open the scoring.
"I could not work out what Arsenal were doing defensively - it was poor," BBC football pundit Alan Shearer said on Match of the Day.
"It was a very good ball by Barry but Mesut Ozil should have stayed with Coleman, who was his man.
"That is not the only mistake, though. There was no pressure on Barry, and you cannot play offside when there is no pressure on the ball."
The Gunners have been linked with Real Madrid's Sami Khedira or Sporting's William Carvalho if they get past Besiktas on Wednesday and secure a place in the Champions League group stage.
Either would make a big difference to plugging gaps of that sort.
Attack: Sanchez not the second striker needed
Wenger spent £35m this summer to sign Alexis Sanchez, who was seen as a step-up from their existing first-choice frontman Olivier Giroud.
Sanchez might well still prove a striking superstar, but against Everton, on his own in attack and leading the line for the first time, he looked lightweight and lost.
"Arsenal had no presence up front," added Shearer. "They had nobody to attack balls in the box. In the 45 minutes he played, Sanchez did not have one touch in the Everton area.
"That all changed, to be fair to Wenger, at half-time when he brought on Giroud. He did have a presence and Arsenal then had somebody who they could see in the box."
But what happens when there is no Giroud? Arsenal could find out again as soon as Wednesday in the second leg against Besiktas because the Frenchman injured his ankle in the closing minutes.
Joel Campbell, who is unproven in the Premier League, and Yaya Sanogo, like Chambers a relative rookie, are their only other options.
And, when you compare Arsenal's firepower to that of the teams who finished above them last season, it appears another definite weak link.
A perfect fit would be a striker with the pace and mobility Giroud lacks, but also the sort of physical presence Sanchez does not possess.
The question is, with Wenger talking after the Everton game about having "more strikers than before", is he even looking for another one? He should be.
A new resolve does not hide the cracks
In each of their three games in the Premier League and Champions League so far this season, Arsenal have been unimpressive. Crucially, though, they have also been unbeaten.
"Very much like last week against Palace, Arsenal did not play well for the vast majority of the game against Everton, but they kept on going until the end and got the three points," said Shearer.
"This week they kept on going until the end and got one point. It was not a very good performance but it is a good sign."
Understandably, after his side had scored two goals in the last seven minutes to get an unlikely draw, Wenger also pointed to their "fantastic spirit" and "complete desire".
"When we got beaten here 3-0 last season, it could have been many more," Wenger explained. "Three was quite flattering on the day.
"For us to come back from 2-0 down this time against a team as good on the counter-attack shows the belief and the resilience was there."
In truth, 'resilience' was what Arsenal had been noticeably short of when they were under the cosh in the first half.
Yes, Everton's second goal was offside, but the Toffees were completely dominant and but for a bad miss by Kevin Mirallas, could have been out of sight by half-time.
What Arsenal actually had, as well as belief, was the ability to rescue something from a game that looked lost, but turned as Everton tired.
Wenger is right to take encouragement from their comeback, and also correct that they probably would not have managed to dig themselves out of a similar-sized hole in the past.
But there is a danger that, in weighing up whether to strengthen his squad in the next few days, he ignores the longstanding problems that mean they needed to.
Perhaps he should remember that not every top team will offer them a second chance.