I predict that Harry knows that the secret to his Father living is Cross-Species Genetics. He knows that Peter is Spider-Man, and has witnessed Spider-Man at his best. The reason Harry has been "away" is because he has been testing different serums on the prisoners. A-la, Aleksei Sytsevich. Harry tested Aleksei with a Rhino serum, and a suit was formed. It worked and Harry was going to modify it for Norman. However Aleksei became crazy, and the side effects for the suit included psychopathic natures. Harry creates an acid that melts the suit off of Aleksei. Aleksei then brakes out of prison, steals a truck and heads for Oscorp, where he steals the Rhino serum back. Spider-Man captures Aleksei and sends him to Ravencroft.
Ravencroft is ran by a man known as Adrian Toomes.
Prior to this event, Peter had discovered his fathers research, and different planned cross species experiments were listed. This is a MAJOR easter egg, as the list includes tests with Vermin, Eels, Birds of Prey, Octopi, Cats, Rhinos and other spidey villains of this nature.
Unable to help Norman, and desperate, Harry hears of the news that a worker had fallen into the Advanced Electric Eel tank and put two and two together once he saw Electro on the news. He then captures Electro, and runs tests on him. Hence the first teaser trailer. Electro becomes super charged and fleas. Harry is then informed that Norman needs a blood transfusion immediately, or he will die. He then realises that the only way to save Norman will be to kill Peter and essentially 'steal' his blood, resulting in Norman having Spider-Man's powers. He then builds a suit for Rhino, (mechanical) knowing he would do anything to become the real Rhino again, and a suit for Electro, giving them the same task - kill the spider. ;)
Electro fails, and is thought to be dead and Rhino is re-captured and sent back to Ravencroft.
Harry recieves the news of Norman's death and reads a letter Norman wrote him. The letter explains that in a secret part of Oscorp he had been working on a super solider serum. Norman states that the serum is close to completion and wants Harry to finish his research. However Norman doesn't mention that the serum has psychopathic side effects... accident? I think not.
Harry tests the serum on himself and becomes the Green Goblin. GG swoops Gwen, forcing her to fall from the bridge, Spider-Man accidentally snaps her neck. Spider-man fights with GG and it is revealed that Harry is the GG. Spider-Man, unable to hurt Harry due to realizing he is not of a stable mind, fleas the scene. The movie ends with GG laughing.
After the credits have rolled a shot of a sleeping Harry is shown. Beside his bed remnants of alcohol and drugs. A man, who appears to be wearing a hat and trench coat enters and leans over a sleeping Harry. He takes his hat off and places it on the bed side table and takes his coat off. It is revealed he is wearing the Goblin armor. He turns around... it's Norman.