Premier League: 37 appearances
Champions League: 9 appearances
Goals conceded/game, all competitions: 0.91
Clean sheets: 20 (16 league, 4 CL)
Goalkeeping is a thankless task. Do it plainly, with no diving saves or spectacular leaps to get the ball out of harm's way, and nobody thinks you're very good. On the flip side, make even one single mistake, and by the nature of your job, you're the goat - if a midfielder makes a mistake, he's got a chance to recover, and he's got a team around him to help clean up the mess, but if a keeper makes a mistake, his next step is usually picking the ball out of the back of the net.
Throughout his time at Arsenal, Wojciech Szczesny has been a lightning rod - a starting keeper at one of England's biggest clubs at the age of 20, he has essentially grown up in goal for Arsenal, and that highly visible maturation process has led quite a few people to think "Arsenal could do better in goal". That thought process thankfully never led to any sort of vitriol, or to #szccout, but there were some in the Arsenal 'verse who thought he wasn't good enough, forgettin that a goalkeeper doesn't really peak until his late20's.
This year, though, Szcz has really taken a step forward - he's cut down the headslapping moments, he's improved his distribution, and he doesn't go walkies nearly as much as he did. I don't think anyone thinks Szcz is the best keeper in the world, or even in England, but he's developed into a reliable first choice for Arsenal, and as he gets older he'll just get more and more solid; Arsenal still need a good backup, but if Szcz keeps improving like he did this year, the #1 shirt won't be available for a while yet.