East HamptonSometime between Aug. 31 and Sept. 6, someone wielding a brick smashed a taillight on a John Deere tractor owned by New York State, parked off Stephen Hand’s Path. Brian Stuckart of the Town Highway Department estimated the replacement cost at $200. Police went to the Empire Gas Station on North Main Street on the morning of Sept. 4 after Turan Turakan, an employee, reported that a customer had offered a counterfeit $100 bill in payment for a $15 gas tab. When confronted, the customer reached into his pocket and presented a legitimate $100 bill. Mr. Turakan, who had already called police, would not give change for the good bill until they arrived. After speaking with the customer, who was not identified, police determined that he was not knowingly trying to pass a bad bill. They confiscated the fake.East Hampton VillageAn East Hampton woman parked her 2002 Nissan on North Main Street in front of the East Hampton Grill at 8 a.m. on Sept. 5 and left it there for about three hours. When she returned, she told police, her iPhone 6, valued at $200, was gone, along with about $35 in cash. She said she would have her daughter use the Find My iPhone app later that day to try to locate it.A Springs woman shopping at Stop and Shop on the afternoon of Sept. 5 left her handbag behind in her shopping cart after loading up her car with groceries. She returned to the store a half-hour later, and a search turned up the bag near the dairy section, sans $400. The store does have surveillance cameras, and an investigation is continuing.Gardiner’s IslandA paddleboarder landed on Gardiner’s Island on Aug. 26 and walked around taking pictures, one of which was posted on Instagram. The owner of the island, Robert Goelet, “wants the subject advised not to return to island, and the picture removed from Instagram to prevent others from entering island,” police reported, but “does not wish to pursue criminal charges.” One of the largest private islands in America, the 3,318-acre Gardiner’s Island was purchased by Lion Gardiner from the Montaukett chief Wyandanch in 1639.MontaukSomeone tried to steal the American flag outside Clinton A. Seyler’s house on West Lake Drive early Labor Day morning but failed to detach it entirely. Mr. Seyler reattached the loose end to the pole. Half an hour later, he told police, he discovered that the thief had returned, and had stolen the flag. Two guests at Ann Breyer’s Cottages damaged a privet bush there last month. James Dispirito told police he did not want to press charges, provided the pair pick up the approximately $500 bill for the damage when they return to Montauk. Police are monitoring the situation.A Facebook page promising “beagle puppies for sale” caught the eye of Julio Lechuga Bolano of South Euclid Avenue, who called and spoke to a man identifying himself as a breeder. Mr. Lechuga Bolano was told to send $560 by Western Union — $530 for the dog and $30 for food. He sent the money on Aug. 25, and it was claimed by someone in Winchester, Va. Four days later, a man claiming to be “airport security” called to say $1,400 more was needed to cover “crate rental and vaccinations,” and promising that most of that sum would be reimbursed after delivery. The money was sent. Another $998 was then requested for insurance. On Aug. 29, Mr. Lechuga Bolano was instructed to go to Kennedy Airport and wait for a call. After waiting all day, his phone rang. The puppy was in Ohio, he was told, and he needed to send another $510 for more vaccinations. At that point he realized he was the victim of a scam, and called Western Union, which told him the money transfers had already gone through. He lost $2,958 altogether. Police are investigating.On the Saturday night of Labor Day weekend, after a town fire marshal entered the Surf Lodge, an employee of the nightspot attempted to “move the crowd,” he later told police. Erin Lynn Tepper of Manhattan refused to comply, he said. Ms. Tepper told police he had slapped her in the face and told her to leave. It was not clear who called police, but the employee was not charged with any wrongdoing.A small group of Manhattaners left Gurney’s in a Mini Cooper without paying for their lunch on Sept. 2. One of them, a man, was caught on surveillance video leaving their $165.11 check “on a bookcase” inside the resort, by the entrance to Tilly’s Restaurant. Surveillance also recorded the car’s license plate, according to the report.A man left his wallet and iPhone 6 Plus unattended on the bar at the Royal Atlantic for about two hours on the afternoon of Sept. 2. When Vito Baccellieri of Pelham Manor, N.Y., went to get his things, they were gone. The total loss, he told police, was about $1,800.A Sanger Place man called police a little after midnight on Sept. 2, reporting that his front porch had been egged, not once but twice. Police searched the area but could not find the eggers.Sag HarborPolice were called to Murf’s Tavern early Sunday morning, where the bartender, Nicholas Carleton, pointed out a female patron who, he said, had punched him in the face after he told her to leave. She had been throwing plastic cups at him, he added. The woman, reportedly intoxicated, claimed the bartender was jealous because she had tried to pick up his girlfriend. No charges were pressed after she agreed to leave. SpringsA Gerard Drive woman told police last week that sometime in late August her mailbox, along with its 4-by-4-inch post, had been ripped from the ground and stolen. Sylvia Witzenmann said it would cost $250 to replace.