Nigel Wilson, 42, from Bingham, near Nottingham, appeared at Westminster Magistrates' Court accused of 17 breaches of the Air Navigation Order.
It is the first prosecution of its kind in England to follow a police-led investigation.
Mr Wilson admitted two counts, but will go on trial for the remaining 15.
Mr Wilson, of Rockingham Grove, admitted two counts of not maintaining visual, unaided contact with an unmanned surveillance aircraft to monitor its flight path.
They relate to incidents over the north bank of the River Thames on September 27 and during Manchester City v Tottenham Hotspur at the Etihad Stadium, Manchester on October 18.
He denied other charges of flying a "small unmanned surveillance aircraft" without permission during football matches at various grounds.
They included Arsenal's Emirates Stadium, Liverpool's Anfield ground as well as Nottingham Forest's City Ground, Derby County's iPro stadium and the King Power Stadium in Leicester.
The charges also claim he breached regulations by failing to maintain direct visual contact with the drone as he flew it near landmarks including Buckingham Palace and the Palace of Westminster.
The majority of the offences are said to have happened in September last year.
Prosecutor Edward Aydin said: "These were extremely busy areas.
"The fear of the police and the Civil Aviation Authority is that it [the drone] is going to fall out of the sky and hit someone."
The Civil Aviation Authority successfully brought two similar cases to court in 2013 and 2014.
However, this is the first time someone has been prosecuted by the Crown Prosecution Service after a police operation.
Mr Wilson is due to appear at the same court on Friday so that a date for his trial can be set.

Davies, 27, who will rejoin Scarlets for the 2016-17 season, missed the World Cup with a serious injury.
He made a try scoring comeback after seven months out in Clermont's European Champions Cup win over Exeter.
"There is a goal but at the moment I'm just concentrating on making sure I'm playing well for Clermont," he said.
"I'd love to get back in the Six Nations squad but it's down to me to make sure I keep working hard in training and perform consistently.
"First things first, I've got to get through a whole game - I only lasted 67 minutes on Saturday."
Wales begin their Six Nations campaign in Ireland on 7 February. Before the tournament starts, Clermont have six games, including three in the European Champions Cup.
Clermont's bonus-point win over Exeter Chiefs threw Pool Two wide open, with all four teams still in with a chance of qualification to the quarter-finals.
Ospreys are top with Clermont in second place ahead of their meeting at the Liberty Stadium in January.
Clermont, last season's beaten finalists, won 34-29 when the sides met in November.
With a game in hand over their rivals, Davies says the French team are in a good position and confident of progressing to the last eight.
"The group as it stands at the moment is quite evenly balanced," Davies told BBC Wales Sport.
"The Ospreys have done extremely well picking up those bonus points when they've come to France twice.
"They're playing some good rugby and ran us close when they came to Clermont.
"We know we've got a game in hand and we have every confidence we can qualify and move forward through the latter stages.
"It's going to be a tough ask but I do feel we've got plenty of quality in our squad to make a stamp on this European competition this year."

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1 April 2015 Last updated at 16:59 BST
Well one man has started using a drone instead. Paul Brennan decided to use one on his brother's farm in Ireland.
The little remote controlled aircraft encourages the sheep into their pen.
Paul says it take three minutes and 21 seconds to get them from one side of the field to another using the gadget.
Jenny's got more on this woolly tech tale...
Pictures from Paul Brennan
A man alleged to have illegally flown a camera drone over packed football stadiums and London tourist attractions has appeared in court.
[NEXT_CONCEPT]
Wales centre Jonathan Davies admits he needs to work on his form and fitness but hopes to feature in the Six Nations.
[NEXT_CONCEPT]
When you don't have a sheep dog, how do you herd your flock?