In his closing speech, Orlando Pownall, prosecuting, told the jury that "instinct and common sense" would tell them there was nothing about the shooting that involved professionalism.
He also said a Kosovan or Serbian gunman would only risk alienating the public by killing someone as popular as Ms Dando - doing their cause no good.
The accused, Barry George, 42, of Crookham Road, Fulham, denies murdering Miss Dando on April 26 1999. She was shot through the head outside her home in Gowan Avenue, Fulham.
Mr Pownall urged the jury to reach their verdict on the evidence they had heard and nothing else.
"You have the responsibility of making an extremely important decision. Do not be sidetracked by theory or speculation or waste time on issues which have no real bearing on the case," he said.
"Bring together your collective common sense and experience of life and follow your instincts."
'Be dispassionate'
He said the suggestion that Serbian terrorists, or their warlord Arkan, were responsible, may have grabbed the public imagination - but the jury had seen the whole story.
"We submit our case cannot easily be dismissed. It is the cumulative effect of the evidence on which we lay stress," he said.
It had also been suggested that the crime had been planned and carefully executed by a professional hitman.
Yet a ballistic expert called by the defence had not addressed the issue of professionalism in any of his three reports, said Mr Powell.
He urged the jury: "If you forget everything else I say, look at the evidence as a whole.
'Eccentric'
"When taken together this evidence leads irresistibly to guilt.
"Whatever your verdict, it will be reached dispassionately, uninfluenced by sympathy for the deceased, her family or friends and likewise, sympathy for the defendant.
"Convict if you are sure of guilt and for no other reason. Acquit if you are not sure."
He asked who would want to kill Miss Dando - she was popular and no-one had spoken ill of her.
There was only one candidate at the end of an exhaustive police investigation, said Mr Pownall.
He told the jury to resist the temptation of reinvestigating the case and becoming detectives themselves.
"The issue for you is whether this defendant was the gunman on 26 April?"
Mr Pownall said the idea that George was a local eccentric being used to satisfy public demand that someone should be brought to justice when the obvious candidate was a Serbian hitman was "utter nonsense".
A "stranger killer" was by no means an unknown phenomenon, he said.
"Unusual as they may be, there are some cases where there is no single motive. How could there be a reason for killing Jill Dando? Sadly not everyone in the world is rational, logical and sensible," he told the jury.
"There is a dark complex side to some people's minds which cause them to act in a dreadfully destructive way for no rational reason."
The trial continues.