NEW YORK CITY—Approximately two in five New York City restaurants, gyms, and entertainment venues weren’t fully abiding by the city’s COVID-19 vaccination pass mandate when first inspected. The city managed to inspect nearly two-thirds of the estimated 31,000 businesses that are required to ask their employees and customers for proof of vaccination. Some 8,000 were issued a warning for noncompliance. Of those, more than 3,300 for infractions that would have led to violations which could be penalized with a fine of $1,000 for the first and going up to $5,000 for the third. Upon second inspection at least two weeks later, only 21 establishments were issued violations, according to Jeff Dupee, City Hall’s senior adviser managing the mandate. Though the mandate allows fines for the first violation, the city has been issuing warnings first “as a matter of policy,” Dupee said, testifying to the City Council’s small business committee on …