Of the 74 breaches, 56 were people travelling into the county - which is in Tier 2 - from Tier 3 areas and not adhering to the guidelines for their tier.
The other 18 were handed out to North Yorkshire residents - including 11 in the Scarborough borough.
Superintendent Mike Walker, North Yorkshire Police's lead for Covid-19, said people have been ringing the force to report others breaking the coronavirus restriction rules.
Police issued 74 fines at the weekend.
He urged people to take personal responsibility for helping stop the spread of the virus, especially at Christmas.
"Even if it's just one day, people need to think carefully if they need to meet," he said.
"We will be doing patrols in the community on Christmas Day. The last thing we want to be doing is enforcing health protection regulations and taking enforcement action on Christmas Day.
"Do we expect to be called out on Christmas Day to a report of a significant breach? I hope not.
"We want the public of North Yorkshire to have as safe, happy a Christmas as possible."
He said extra patrols will be out on New Year's Eve to ensure the night passes off peacefully, but asked people to consider celebrating the end of 2020 at home.