Keep patients happy, send less patients to Auto Autopsy, and cure more people than you kill. That's basically the recipe for not getting the bad newspapers and stuff. The newspapers are usually random and not based on what you've actually done in the game, other than killing off people and sending them home seems to be the trigger for losing the game and triggering the newspaper with the bad headline.

Have more than enough doctors, keep them happy with enough heating, lots of space and items in the rooms, always build a large staffroom, have enough handymen to keep the hospital litter-free, have open spaces in the hallways to prevent epidemics and vomit-fits, have at least two receptionists on later levels, build more than one of each diagnostic or treatment room, and keep fixing or replacing treatment machines. Drinks machines and benches should be placed everywhere, and radiators should be placed around five blocks apart on every wall to keep the hospital warm enough at all times.

Good luck :)