John Kane filmed more than 60 women in the Central Retail Park and a nearby supermarket last July.
The 67-year-old also secretly recorded children playing outside a nearby Next store.
Kane was placed on the sex offenders register ahead of sentencing on 30 March at Falkirk Sheriff Court.
Prosecutor Ann Orr told the court that Kane tried to flush a memory card down the toilet at a police station after being arrested for drink driving.
The memory card contained 60 short videos, lasting between 50 seconds and three minutes.
Mrs Orr said: "The recordings appeared to be of adult females at various shops in the Central Retail Park.
"The camera operator has the camera positioned to show the females from the waist down, focusing on their bare legs and zooming in on their bottoms."
The depute fiscal said the memory card also contained three slightly-longer videos showing children aged between six and 12 playing.
Mrs Orr said: "One child is doing cartwheels, and the camera zooms in on the crotch area."
Mrs Orr said the camera operator's distinctive cream, leather-toecapped trainers and khaki shorts were in shot in many of the videos.
She said Police Scotland received an anonymous phone call from someone who expressed "concern" over Kane's behaviour.
A search warrant was obtained for his home, and the khaki shorts and distinctive trainers were found in a bag in his spare bedroom.
Kane told police he "had a drink in him" at the time the videos were filmed.
Asked if what he had done aroused him, he said: "It did at the time, but afterwards I felt ashamed about it."
Kane, of Falkirk, admitted operating a recording device to obtain footage of women and children in a public place without their knowledge and consent between 15 July and 22 July last year.
Sheriff Derek Livingston deferred sentence for a risk assessment and released Kane on bail.
A pensioner used a mini camera to secretly film women's bare legs in a Falkirk shopping centre, a court was told.