How to deal with the "undercover cop unearths den of crime" message?

First of all, click that cross (the one next to the message) to dismiss it. More than likely the problem is already dealt with, but the message hasn't gone away yet (if it returns then you do have a problem - if not, all good).

If you do have a problem, all you can do is increase the police presence / make crime unnatractive. That means you can:

• Increase funding of existing police stations (Bigger Police Presence)
• Create more Police Stations (Bigger Police Presence)
• Remove Gambling Laws (Lowers Crime Attractiveness)
• Have an Educated Populace (Lowers Crime Attractiveness)
  • Invest in Universities, Libraries and School
  • Make it so the rich demographic dominates your city
• Adapt your buildings to counter the type of crime
  • eg: If there are a lot of shoplifters, rezone commercial areas as residential/industrial
• Create Roads so the Police can actually get to the buildings being targetted

I have found out it's a game bug due to the large tile objects. The police can't penetrate beyond three tiles. So the solution for the airport is to surround it with roads (do this for all large tiles such as the golf course, university, etc), place a deluxe police station at both long ends around the middle, and a police kiosk at every corner. Also as others said make sure your sims are educated and after awhile you won't have either crimes or fires. If crime persists at the airport and messages drive you crazy, anyway, blow up the airport and let the game run a month, then put it back. Goes for all large tiles that keep having crime messages regardless of police stations nearby. It means the game has randomly put a crime in a center tile where police can't get to so it remains unsolved.