From what I've seen from talking to Arsenal fans it's the chronic lack of investment and more importantly ambition during his tenure at the club. We've all seen how the squad has been whittled down, some very good players like Fabregas, Van Persie, Adebayor, Toure, Song, Clichy, Nasri, Flamini, Henry even going back to Vieira have been sold and not replaced. It's not so much the fact they're sold, as sometimes the financial offer has been too good to resist or there are other reasons for the player going, but more the fact they've never been adequately replaced.
In the last 5 or so years the only ambitious signing they've made has been Arshavin - it's the only time they've signed a player recognised to be of immense talent and also a player at the top of his game when they signed him. Sure there have been some good youth signings, the likes of Wallcott, Ramsey and Chamberlain, but these have been signing prospects and not players who were ready to take the team on immediately. There was a mini-flurry of fairly good signings after the disasterous start to last season (big defeats home to Liverpool and away to Man Utd) but Mertersacker and Arteta, while reasonably good players, are not really stellar footballers.
What doesnt help is that talent has been allowed to leave prematurly because of their age and wages. Would it have killed the club to have given Pires or Gilberto Silva another two years on their contracts when they left the club? Even players like Lauren and Campbell could have made the difference and would have been great backups to have when they left.
A lot of these issues were set in motion before Kroenke came in, but the weakening of the squad and the stagnation of player purchases have really accelerated under his tenure. I can appreciate that the likes of City, Chelsea and the Spanish two can beat Arsenal when it comes to signing players - Mata was probably going to be an Arsenal player before Chelsea stepped in. But there are still a lot of quality players on the market at reasonable (while in footballing terms "reasonable") prices, whom Arsenal should be able to afford given the money they've recouped in transfers over the last few seasons. Falcao wa signed by Atletico last season, there is no reason why Arsenal couldnt afford to go for him given the money they had got in previous seasons. In the last few years Spurs have signed players like Van Der Vaart and Dembele, Milan have signed De Jong, Liverpool have signed Suarez, Kiev signed Veloso, there are some excellent players available for moderate fees, yet Arsenal have just been treading water in the transfer market. I'm not saying they should go out and buy player after player, but their current policy smacks of lack of ambition. I don't see how at least some funds cant be there, the stadium loan is almost totally paid off now, there have been massive in-flows via transfer fees and the club charge the most for tickets in the UK.
And while it might be true to say that finishing 4th is reasonable given the resources of Chelsea and City, it really shouldnt be banded around in public repeatedly as some sort of trophy. It's simply isnt like a trophy - if Arsenal were to finish runners up in the League or the CL that would constitue a reasonable season, but if they finished "runners up" in the battle for 4th place (i.e. 5th) it would be an underachievment and disaster - so equating it to a trophy is, in my opinion dangerous, it more like a minimum standard, like Fulham saying that Premier League survival is a minimum standard. This together with the lack of transfers, hints at some sort of managed decline which Korenke seems to be encouraging or at the very least incapable of halting.
Arsenal are a great team, 5-10 years ago they were one of the top 2-3 clubs in England and easily the biggest club in London. They were signing world class players like Bergkamp, Platt, Overmars, Petit, Gilberto Silva, Jens Lehmann. They hardly ever seem to sign players like that anymore and they are in danger of slipping into mediocrity.
then all Arsenal! 
