There is an area of thought which says that Arsenal's 1-1 draw with Manchester United was a bad result and highlights the club's lack of 'ambition'. That seems an odd argument: Arsenal have not won a league game at Old Trafford since the 2006/07 season, and have just two points in the 8 games at Old Trafford since that 1-0 victory, including last season, where they lost against David Moyes' Manchester United. Furthermore, whatever you think of the quality of Louis van Gaal's £150m outfit, of the top 6, only Arsenal and Chelsea have taken points from United at Old Trafford: Manchester City were thrashed, Liverpool were well-beaten, and Tottenham, well, it's Tottenham. Given that context, and given that Arsenal only really needed a point, the 1-1 draw against Manchester United is certainly not a bad result. Having said that, Arsenal were very poor for the first hour of the match, and were fortunate that United aren't that good; otherwise, they would've been more than one goal down by the time the rescue mission got going.
Arsenal's biggest issue in the first half was represented by not creating a single shot. Unable to pass the ball through the midfield, Arsenal resorted to going long. Arsenal were unable to pass the ball through midfield because they still struggle against teams that look to press heavily, as United did, with Fellaini and Herrera sticking to Coquelin and Cazorla, and Blind occupying Mesut Özil, or letting one of the centre backs mark him if he looked to get behind. Furthermore, neither Aaron Ramsey nor Alexis Sánchez occupied the width: Ramsey because he is a central midfielder, and Alexis because he's let his playmaking side get the better of him in recent weeks, an issue that is less prominent when he is on the right hand side.
However, it was Arsenal's central midfield that were the biggest offenders in the first half. Francis Coquelin's defensive work in the past 5 months has been vital, but it is hard to get away from the feeling that if Arsenal are to truly compete for the Premier League title, they'll need a holding midfielder who can both destroy as well as control. Coquelin does not do that.
As ArsenalColumn noted, Coquelin does not contribute to build-up play, and does not offer himself to the centre backs. When facing defences that are not great, that is fine: Koscielny and Mertesacker are more than adept at passing through to the midfielders (just see, for example, Arsenal's opening goal against West Ham in March), but against better opposition, such as Swansea, Arsenal need the passing capability of a Mikel Arteta/Xabi Alonson/Sergio Busquets/Javi Martinez. This is also shown in how Arsenal have not been able to control the midfield for large portions of matches this season, unless Santi Cazorla, deployed in central midfield because he is adept against pressure and Coquelin is not, can play further up the pitch and combine with Ramsey and Özil. Because of that, it seems fair to argue that Coquelin is not 'the answer', and should be Arsenal's biggest priority this summer, not least because a controller will allow Ramsey to play in the middle again, and Arsenal are simply a better side when Ramsey is central. It seems unlikely that the first goal would've been conceded had Ramsey been in the side, but the runs of Fellaini and then Herrera were left unattended by Coquelin and Cazorla, allowing United to create an overload.
Finally, Arsenal still have work to do on the creative side of the game. Last season, Arsène Wenger felt that the side needed to score more goals, and it is likely that he'll feel the same again: at 67 goals in 36 games, Arsenal are scoring at a slightly higher rate than last season, but not scoring enough. Wenger will likely look for an upgrade along his front line. Given that signing a player of the quality of, say, Sergio Agüero is nearly impossible, Wenger will probably look to sign a creative, but goal-scoring, wide playmaker in the mould of Robert Pires. Alexis is not that player; Alexis is an upgrade on Theo Walcott and a possibility to become an exceptional centre forward, but his contribution in build-up play is too disruptive for him to take on a playmaking role. On Sunday, he lost the ball 16 times from 39 touches, a rate that is simply not good enough for a possession side. Alexis has had a great first season at Arsenal, but the past few months have been patchy. He'll likely have more of goal-scoring job next season, and less of a playmaking one, given that Mesut Özil will hopefully be fit for the entirety of the campaign, but that'll only come to fruition if Arsenal sign a playmaker for the left-sided spot.
Arsenal are not far from where they need to be to challenge for the Premier League, and the business of the last two summers has put them at a place where they only need slight upgrades rather than massive change: a keeper, a midfielder, and a wide player. Assuming that business can be done, and there is no reason why it shouldn't, given the money Arsenal now have, Arsenal can look forward to their title challenge being over a full season, rather than a product of half a season of good form.