His tweet simply said "Day 3 #happybirthday" with a photo of a metallic locker. While this may seem like an innocent tweet, the lockers themselves could spark some memories from fans of Brian Michael Bendis' Ultimate Spider-Man series of comics and the origin story of Venom.
In the Ultimate Spider-Man continuity, the Venom came from scientists Richard Parker and Eddie Brock searching for a cure for cancer. The experiment was deemed a failure and it wasn't until after they had both passed that their children Peter Parker and Eddie Brock Jr discovered the protoplasmic dip in an Oscorp locker.
Couple this with Webb's tweet from day 2 of production which showed that the movie was returning to Oscorp and we could be nearing a reveal that Eddie Brock will be joining the ever expanding character list.
However, February marks the 25th anniversary of the Venom character who first appeared in The Amazing Spider-Man #299. So this could just be a clever in-joke from the filmmakers.
Already set for The Amazing Spider-Man 2 is Jamie Foxx (Django Unchained) as Electro, Shailene Woodley (The Descendants) as Mary-Jane Watson, Paul Giamatti (Sideways) as the Rhino and Dane DeHaan (Chronicle) as Harry Osborn. They will join the returning Andrew Garfield (The Social Network), Emma Stone (Easy A), Sally Field (Lincoln) and Martin Sheen (The West Wing) for the movie set for release on 2nd May 2014.