To start with, I think a shake-up is board level is needed. Bring in some fresh faces, because with fresh faces comes new ideas and that can't be a bad thing. Also, whilst on the topic of behind the scenes work, additional work on commercial income because we lag so much on the clubs around us in this aspect it's not funny.
Keep Wenger as manager, I think the job he is doing is the least of our worries right now. If he gets suitable backing in the market I'm confident he'll get the people in we need. However, I think some of the load needs to be taken off his shoulders and he needs to let other coaches do coaching. Have specialised defence and attacking coaches (Bould and Pimorac?) which lets Wenger just do what he did before and just focus on managing the team on the pitch.
Now for players. Get rid of as much deadwood as possible. Fabianski (very good keeper but wants to be first choice elsewhere), Djourou, Squillaci, Santos, Denilson, Arshavin, Chamakh, Park, Bendtner. In total thats maybe £10 million in fees + approx. £300k off the wage bill. If Diaby doesn't prove he can put a string of games together between now and the end of the season, cut him loose. If Sagna doesn't want to sign a contract extension, sell him.
As for the incoming players. A GK is needed, someone who will give Szczesny a real challenge (Begovic or Stekelenburg), if Sagna goes a RB would be needed (in honesty I don't know of any top-line RBs out there we could get, Aurier from Toulouse would be a good buy if we went for a young guy to give Jenkinson direct competition), a top-class CB is a must and should be number 2 on the priority list behind a striker. I'd look at Hummels but being realistic Nicolas N'Koulou from Marseille would be a cracking buy and would give us 4 top class CBs. A holding midfielder in the mould of Wanyama or Capoue is required. As for a striker, my ideal buy would be Jovetic. That leaves us with a superb starting XI with plenty of competition for places, although maybe an additional midfielder and striker could do to just add some more depth.
Tactics-wise, have a genuine Plan B. And I don't just mean play a big man upfront so we cross it a bit more, adjust the midfield - have the two holding midfielders sit deeper especially Wanyama/Capoue to break up attacks and quickly give it to Arteta/Wilshere/Cazorla to quickly counter the other team. Too often we go to the Manchesters and Chelsea and just assume we can play our normal game and it will be enough but other teams read us like a book. Shake it up a bit.
Oh and make Arteta captain with Wilshere his deputy. Captaincy has ruined Vermaelen and he shouldn't be guaranteed a starting berth because of it.