So I rewatched most of Season One. I figured the skippable episodes were 0-8-4, The Asset, and Repairs. It quickly became clear that season one is actually much better paced than I remembered with those early episodes setting up pretty important foundations. The episodes that might have mattered the least were FZZT and Yes Man and both were good episodes (the latter was the first to involve a non-SHIELD character from the movies).
Having watched it with the benefit of hindsight, it's absolutely clear that they knew the twist in The Winter Soldier from the beginning. There are lots of subtle references. Akala Amador in Eye Spy said that she was locked away. She thought the people who rescued her were SHIELD agents. I believe it was that episode where Ward says something like "imagine being betrayed by someone you trust." They also make their Night-Night guns from dendrotoxin, which is the same stuff Fury uses to fake his own death.
Speaking of, I'm pretty sure my first post here was a post about the timeline of The Winter Soldier. I'm convinced the only way it makes sense is if the events seen in the show happen early on and the Hub, Academy, etc. fall before the Triskellion. The Winter Soldier clearly takes place over three days. The night of the first day is when Fury gets shot and "dies." The events of Agents of SHIELD happen at night. Simmons notices commotion at the Hub and everything goes crazy, Fitz discovers May's secure line to Fury, and when they call in, they find out Fury is dead. Day two, Hydra has secretly taken over the Triskellion hunting Captain America, and day three involves Steve taking down Project Insight. I just don't see the events in the Hub taking two days. However, after the Hub falls, there's a pause after Garrett is arrested before they cut to the scene about the recap at the Triskellion. It also can't be that the events of Agents of SHIELD happen on day two or three. They were heading to Washington because Fury called them after resurfacing. That had to be around the time he was in DC, talked to Pierce, and was attacked and called for Hill.
It's not crazy to imagine that Triskellion operated after the other places fell. The signal to come out of the shadows was scrambling communication, so people couldn't reach other SHIELD bases. Similarly, the people in charge of communication could have been Hydra. And day two certainly wasn't business as usual, even if people didn't know that Hydra had taken over. They were hunting Steve Rogers.
Just my take on everything.