Well, the weatherman has just made MANY mistakes with this last hit, any one of which can usually lead to a culprit being caught.

1.) He attacked a highly populated area where people are coming and going. This is like the equivalent of the ball dropping in Time Square, and an international pop idol is a known guest, so somebody's bound to be filming for local news. The press will be all over this guy and there will be many potential witnesses even though he's sniping from far away.

2.) Unless this guy has some serious freaking connections, the shell left behind by that sniper rifle should be pretty easily traceable, and can potentially turn up a positive ID on his identity. 

3.) One shot at a difficult angle will make it very easy for forensics investigators to pinpoint the origin of the shot and investigate where he fired from.

4.) No rain to wash away the evidence. One bootprint is all it takes to figure out that your suspect is literally the largest person in shine city. Investigators will have a narrow list of suspects to close in on. 

5.) Inadvertently targeting a high-profile wealthy family. The Mochizukki family has the financial resources and thus political sway at their disposal to warrant a long-term high-expenditure investigation. This will NOT be laughed off like some random DJ's suspicions (sorry Nori). Couple this with the fact that he attacked town hall, which is presumably state or federal property, and the police are gonna throw everything they have at this guy.

6.) He chose New Year's Eve, the one day of the year where literally everybody is up and about at midnight. Use this as a multiplier for potential witnesses. 

7.) From what I can tell, the M77 sniper does not appear to have much silencing. The noise of the shot will make it easy to identify the origin and will also serve as another witness multiplier. 

So, in short, if this guy isn't caught within 24 hours, every officer in Shine City should resign for incompetence.