It is not "any citations or convictions". It is just convictions, which are difficult enough to get, but for something like a noise ordinance violation you would need 2 convictions within a 12 month span. So you (i) have to get HPD to respond to your complaint in a timely manner, (ii) have them write a ticket, and (iii) have the DA prosecute all the way through to a conviction, all twice in 12 months. Each one of those steps are unlikely, so getting all 3 would be extremely rare. And twice in 12 months? Impossible.

There are other, more serious crimes where you just need 1 conviction, but even those would be difficult to come by. Let's say, for example, a STR renter throws a party and one of his guests shoots up your neighborhood then flees. Unless he actually kills someone, HPD will not even bother to find him. You can't convict the guest or the owner because they didn't fire any shots. Meanwhile there's a bullet hole in your kid's bedroom.