Actually against dortmund they didn't play like shit. It was an evenly balanced game in every sense of the word. The dortmund game was somewhat similar to the chelsea game. Arsenal conceded a sloppy goal from a defensive error, dortmund capitalized, leading arsenal to over-commit and get punished on the counter-break. Dortmund started well but arsenal ended up controlling major portions of the game.
Point is, when you're 1 nil up, with or without 10 men, whether you're chelsea, united, or any other top team in the premier league you run the risk of the opposition snatching a goal and getting a result. If you manage to escape that as a team than it's a job well done, hence the importance of the 'two-goal cushion'. Arsenal weren't brilliant against a very compact side playing with two walls of 4, went down to 10 men, and managed to put the game to rest. That for me, again, is an excellent response.
Whether or not they have the squad depth to get the premier league is yet to be seen. As I said before, I don't think so. I think our best chance is one of the cups this season. Consider the following though:
Arsene is the longest serving current premier league manager
All other top teams have gone through some dramatic change of some sorts
Arsenal have had the most time to gel as a team
Arsenal have picked up the most points than any other team in europe since january
Arsenal have one of the best defensive records since the beginning of last season, in europe.
This is why the table is the way it is now, with teams like spurs, arsenal, and liverpool having the upper-hand.
Sometimes there's this disillusion that everything that isn't arsenal is great. Maybe it would be refreshing for teams to look at the players that they've got instead of consistently looking at what they haven't got. They seem like a compact unit at the moment and are playing some brilliant football. The next few weeks will tell us everything we need to know about their credentials in any competition.