So I think it can be summarised in a few points
He says in interviews like yesterday that "he has £300m to spend on the right players, should they become available", or words to that effect I believe. The problem that I saw someone say is that the best players like Pogba and upwards are all unavailable, but the best clubs make them available by splashing the big cash. If he has so much money, but only for world class talent, spend 150m on aguero, spend 120m on lewandowski etc. The quote makes no sense, and sounds like a way of defending tightness. How can you say you have money available for the right players, but then look at players who you think are "right" for the club, and then negotiate yourself out of the deals.
Secondly, a lot of the fans would argue that "buying players just to satisfy the fans" is a bit of a simplification, if they pay such exorbitant ticket prices at the Emirates stadium, you'd expect that it would be going towards players.
Bringing me onto the third point, that the emirates stadium was meant to bring bigger players to the club, as a downside of losing the historic/cultural significance of Highbury. After years of transfer windows when they were told that they had lots of money, but needed it to pay off the stadium etc. Being told that they have hundreds of mil to spend now, but at the same time, are playing essentially youth players in their debut against Liverpool on the first game of the season, really don't sit well together.
Adding to that, many people felt that Arsenal should have won the league last season, and before it started, they were still saying Arsenal needed a striker and a CB. Arsenal didn't win the season, (not much surprise for most), and now it looks as though they will go into the season exactly the same, but actually having lost some of their players (Rosicky, Flamini, out, Ramsey/Welbeck injured so far etc.)
Additionally, there are many players who are at the club on very high wages like Theo Walcott. One of the reasons he is being used as a scapegoat is because they feel like they could sell players like him, and replace them with ones who score goals, what arsenal need. The simple fact is that even in his recent transition to a more central, striker role, he has only had one breakout season in 2012 where he scored 21 total goals, and since then, has scored 22 goals in his last 81 games for the club. That is not a record that a top 4 striker should have, considering the competition nowadays in the top 6-8 of the table.
I think the main essence can be summed up that Arsene comes across as though he does good business. But in another thread I actually investigated the transfers as seen here, and as you can see, he has lost £179m and only made £407m back in sales from the £587m that he is spent.
For me, the biggest issues of concern are replacement of top talent. It's easy to see why fans of Arsenal complain when to replace their Captain/Top Goalscorer/One Of Best Players in Van Persie (sold for £22m), Arsene had Podolski, Bendtner, Giroud, Gervinho, all for about £10-15m each and Park Chu Young for £5m he then let Bendtner, Podolski, and Park Chu Young go on free transfers, lost £3m on Gervinho, and then whatever happens to Giroud.
As a result, Arsenal basically Lost their Captain/Best Striker for the +£22M they gained, but - the 35M on players, and the £13M extra that they still have on Giroud.
They basically went from having Van Persie banging in 37 goals in 48 appearences, and paid £26M to swap him for Giroud. (Obviously Hindsight is 20/20).
Meanwhile, Arsene is paraded in the media as if he buys well and invests in young players and sells them on for bigger sums, when in reality, when you look at the transfers even briefly, it rarely seems to be the case.