Barry George took 4,000 photographs of women, whom he followed and harassed in Fulham, south west London, where Miss Dando was shot dead on her doorstep in April 1999, jurors at his Old Bailey retrial were told.
He was originally tried for the killing in 2001 and denies murder.
Jonathan Laidlaw, QC, prosecuting, in his opening speech, said that Mr George was "fixated with the famous and with celebrities" and had a particular "fascination" with female television personalities, including Anthea Turner.
The 48-year-old, who once worked at the BBC as a messenger, had mental health problems and was also known to have stalked women in the streets around Fulham, where he and Miss Dando lived, for more than 15 years.
Eight women claim they that they were repeatedly watched and harassed on their doorsteps, or as they walked home. Mr George threatened one, telling her "I know where you live", and became aggressive with them when he was rebuffed.
Mr Laidlaw said: "While others in Fulham might have regarded the defendant as a lonely, harmless individual, there is evidence of a more sinister aspect to his pursuit of women".
Mr George also has a strong interest in weaponry and the military "that extends far beyond curiosity", the jury was told.
A photograph of Mr George found in his flat showed him wearing a gasmask and holding an adapted pistol consistent with the kind used to kill Miss Dando.
He had been in the Territorial Army and enjoyed wearing combat gear and firing weapons, the court heard.
Two weeks before Miss Dando died, Mr George allegedly bought a number of military items. He was said to have boasted that he was ex-special forces and he once "stormed" a friend's home and fired blank rounds from a handgun. Others allegedly knew him to have a machine gun, a handgun, and another silver handgun.
Mr Laidlaw said Miss Dando's murder was the work of an irrational "loner".
The gunman shot her at point-blank range outside the door of her home in Gowan Avenue, Fulham, on 26 April 1999.
Miss Dando had arrived moments earlier from the nearby home of her fiancée in Chiswick. Mr Laidlaw said that the killer was not a burglar, a street robber or a professional hitman.
"On the contrary, the murder was, so the prosecution suggest, the work of a single individual, a loner, a man acting alone, with no rational motive to kill".
The court heard that Miss Dando had been taken "entirely by surprise" after the gunman approached her from behind as she was about to unlock her door.
She was either pushed down or in a crouching position when the assassin put the gun "firmly" to her head and fired it.
A neighbour, Richard Hughes, heard a five-second scream.
The 9mm bullet passed through her head and was recovered on the doorstep. The gun was held so tightly to her head that it muffled the sound of it firing.
Six witnesses living in and around the area identified Mr George as a man they had seen hanging around Govan Avenue the night before and on the morning of the murder.
Mr George lied to police and changed his alibi, claiming originally that he was at home at the time of the murder, but later saying he was at a disability support centre in Hammersmith, Mr Laidlaw said.
The prosecution believe that Mr George returned home after the murder and changed, then deliberately went out again so that he would be seen wearing different clothes "in the hope that suspicion would not fall upon him".
Mr George sat in the dock wearing a pale blue shirt, alongside Dr Susan Young, a blonde-haired clinical psychologist.
The judge, Mr Justice Griffith Williams, said that she was there "because the defendant suffers from epilepsy and has psychological problems which make it difficult for him to follow proceedings".
Barry George's sister, Michelle Diskin, was also in court.
Mr Laidlaw said that Mr George and the high profile case had attracted "many different views, opinions and theories" over the years.
"What has gone before now no longer matters," he said.
The case continues.
