Time to clear up a little of the confusion I see running around! Shenice93 to the rescue!
First, yes having offended someone can indeed cause your Sim to be falsely accused. It has happened to me many times before. Sometimes it's annoying when it happens to you kid Sims as they can't get rid of it most of the time.
Second, there are several ways to get rid of the false accusations (and the moodlet that comes with it). One way is to pay of the paparazzi. You do this by going to the business office. That can be pretty expensive, but it's a sure way to work. You can also redirect the scandal onto a celebrity you know (at same location). This sometimes works and sometimes doesn't. You can disperse rumors by simply talking to people in town and choosing that social option. This depends on your relationship with that particular Sim and takes a couple of uses to completely get rid of it. Then there's the option to sue for slander at City Hall, for a fee of course. This, like redirecting the scandal,, works sometimes and sometimes it blows up in your face.
If your celebrity Sims live in large houses like mine do and always have a large amount of moodlets on their panel, then the 3 day "Publicly Disgraced" moodlet doesn't really make a huge dent in your celebrity's moods. If it does you can always go to the "moodlet manager."
And to keep paparazzi out of your house, build a fence and use the electronic gate. Leave no openings! Make sure you completely surround your house. If you don't well your newly wed celebrities won't get the peace they need to bring in the next generation.
Finally, whether or not late night appeals to you depends on what you want out of the game. Personally, I feel the celebrity freebies, vampires and clubs outweigh the negative effects of being a celebrity. Besides, when my Sims are swimming in more money than I know what to do with then I can just pay off the paparazzi every time it happens. But it still depends on you personally and your interest.