If these minor offenses are not affecting crime then are they offenses whose only purpose is to generate revenue? If the city has not imploded then is that not sufficient evidence to get a discussion about the existence of these offenses?
I would guess that there hasn't been enough time for people to realize their minor infractions will no longer get punished.
1. People speed and park wrongly despite both of these being illegal
2. A huge majority of people aren't assholes all the time, despite this not being illegal
3. Murders do get committed though it's illegal
4. Most stuff isn't stolen even though it is very difficult to catch someone breaking into houses
There's a book called Three Felonies A Day which posits that the average American commits three serious crimes every day despite the overwhelming majority of those folks not meaning to. https://www.google.com/webhp?#q=three+felonies+a+day The reason for this is that the laws are written broadly enough that entirely innocent acts could be construed to be strict-liability crimes that require absolute adherence; intent does not enter into the equation.
If society is not falling apart even if the average American is in fact committing three felonies a day, then it stands to reason that perhaps the law as a whole is over-written and could stand to be reduced. This new informal policing policy in New York might end up being further evidence of such problems.
Further people have found that in many cases persuasion is much more effective than compulsion. In the UK they've found that they can replace speed cameras (which issue tickets) with radar controlled signs that display smiley or frowny faces and that's much more effective at getting people to slow down. The theory goes that compulsion is a very ephemeral threat and that the police can't be everywhere at once ticketing everyone who's speeding all the time and people know it. But just asking them to slow down with no threat is more effective since it's polite.
https://www.google.com/webhp?q=speed+cameras+persuasion+comp...
A similar theory was used to great effect by King Frederick of Prussia to get people to eat potatoes. Decrees did nothing to make people plant them, but declaring the potato to be a royal food and nobody but the king could eat it caused people to plant it either out of spite or a desire to flout the rules. http://www.historynet.com/ask-mhq-king-frederick-ii-of-pruss...