nitpicking part got me thinking though.
1. Nick Fury thought he was in a safe place and obviously he had on some form of vest because he survived. When he got shot in Avengers it was by a piston. When he got shot in Cap2 it was with a high powered rifle. Maybe his vest could only withstand a certain caliber bullet before it loses some integrity.
2. Tony Stark uncovered shyt like the Hydra weapons which should've been enough to cause red flags. But understand it's been 60 years. In order for Stark to see everything, that would require everything being connected to a network. Maybe Hydra kept everything on remote servers.
3. If Hydra has been infiltrating shield for that long... it wouldn't be that hard. I mean they infiltrated shield back in the first captain america. Red Skull was a member of shield so he knew how they operated. Hydra was birthed from shield.
4. The teserat was valuable but that's only used for time travel and making weapons. But remember, they only just got it in The Avengers. And Shield/Hydra did continue to use it to make weapons, using Thor as an excuse. And now they have the mind gem.