Given the clues in the episodes it must be around June 29th - 30th, 1969. They found a Delivery slip of paper that says June 10, 1969 and then later say it was a full moon which will put it at the end of the month. June 10th would be going into New Moon.
Scooby and Shaggy went to see Star: Dog Ranger of the North Woods - probably an animated film and about an hour and half. They saw it twice. So if the movie started at 6P for the first showing and second was at 7:45P. They started walking home around 9:30P. From other Scooby Doo related material they are in Coolsville which is probably an area of Los Angeles. When they find the Knight and the abandoned truck they went and got the other gang members which would be get them out late around probably 11P. The next day they go to the Los Angeles County Museum of Art. Break into the Museum that night and solve an art counterfeit ring that night getting Sheriff Peter Pitchess involved at the end as he was the Sheriff of Los Angeles County in 1969.
Scooby and Shaggy went to see Star: Dog Ranger of the North Woods - probably an animated film and about an hour and half. They saw it twice. So if the movie started at 6P for the first showing and second was at 7:45P. They started walking home around 9:30P. From other Scooby Doo related material they are in Coolsville which is probably an area of Los Angeles. When they find the Knight and the abandoned truck they went and got the other gang members which would be get them out late around probably 11P. The next day they go to the Los Angeles County Museum of Art. Break into the Museum that night and solve an art counterfeit ring that night getting Sheriff Peter Pitchess involved at the end as he was the Sheriff of Los Angeles County in 1969.