Given a certain set of events from the movie and carried over to the TV show, there are some things I'm wondering about. Massive spoilers for both Captain America: The Winter Soldier and the most recent episode of Agents of SHIELD.
So SHIELD was basically a front for HYDRA. From TWS it's pretty clear that SHIELD in its current form is being dismantled. But that's still in the future in relation to AoS. The show is just past the point of the downing of the helicarriers. But that's not the end of the movie. Steve Rogers was in the hospital for an unknown period of time and there's another unknown period of time before the scenes at Fury's grave, Stark Industries and the CIA.
I didn't expect the battle with HYDRA to be over immediately after Cap and Falcon took down the helicarriers any more than the Galactic Empire immediately ceased to exist when the second Death Star went boom. So I'm glad AoS is dealing with SHIELD's internal war with HYDRA. Presumably that war will take up the rest of the season.
A big question is who is in charge of SHIELD during the war. Fury is still presumed dead as far I know. I think Maria Hill went dark after helping Fury stage his death, which would explain why Hand thought she and Coulson were the most senior SHIELD agents around. But it's a safe bet that Fury and/or Hill will pop up at some point.
But there's still the question of what happens to SHIELD. The movie shows that Fury, Hill and others have moved on from SHIELD. Fury is probably going to try to put together a new SHIELD (maybe in time for the Avengers to assemble again). So the SHIELD that Coulson and his team are a part of is finished. Fury and Hill wouldn't have moved on if they thought the current SHIELD was salvageable.
And what happens to all the high tech gear, alien tech and bad guys that SHIELD has in its assorted facilities?
What happens when the timeline on Agents of SHIELD catches up to the final scenes of Captain America: The Winter Soldier?
Finally, how will HYDRA figure into an Agent Carter show? Will there be the undertone of doom? Will we see Toby Jones showing up and doing a Darth Sidious bit?