Before everyone goes crazy and starts yelling: go away forever, delete the game, why are you here, etc., let me preface this by saying I loved season 1, and I was engrossed through all of S2E1. If I had to rate it I would give it a 9/10. From the moment Omid takes a bullet I was hooked (and almost cried).
Now, I do think the puzzle aspects of the game could use SERIOUS improvement.
As someone who has played a lot of story driven puzzle games (e.g., Kyrandia 1-3, Goblins 1-3, original Sam and Max, all the Monkey Islands, etc), there are various suggestions to be made that would improve the game. For instance, when approaching a boarded up deck, the option shouldn't automatically be there for you to use your hammer, this removes the puzzle aspect. Instead you should have to cycle through your item menu and figure it out. You should also be able to get ahead in the game without item X, and then have to backtrack for it as someone previously suggested (i.e., let me leave the shack without the hammer). These are pretty standard game mechanics, dating back to Full Throttle, Day of the Tentacle, etc. these are reasonable improvements, that were available in the 90s on DOS based games!
Maybe add in some item combination? For instance, instead of Clem just laying all the items out on the work deck to clean her arm, make us combine them in the right order and figure this out on our own.
I love the story, I love the writing, the narrative, I was perfectly fine with the action sequences, I just think the puzzle and item aspects are Pre Windows 3.1 and DOS based gaming, which is kinda pathetic in 2013.