A 21-year-old has been arrested and charged over the incidents, which have been reported as happening at local sports grounds, public toilets, churches and schools.
Police have thanked members of the public who helped them identify the man by alerting them to suspicious activity.
"It's a timely reminder to always report unusual behaviour to police as soon as you notice something. Your information might just be the missing piece of the puzzle we need to help stop further offending", police said in a statement.