A lot of people aren't really liking this card, particularly with the one influence cost. As Zakalwe points out, if you're only making a run or two per turn, Net Celebrity pays off much faster. So what gives?
They're missing something significant. Bad publicity scales quadratically.
Bad publicity gives you a discount on every run you make. Increasing the amount of bad publicity you have means that you both save more per run, and runs are cheaper, letting you make more of them.
Consider this. The corp has a single Eli 1.0 protecting R&D, and you have a Corroder or Eater and a Keyhole. You just played a Day Job and have 10 credits and want to hammer R&D. How many times can you hit it before needing to click for credits?
0 bad pub: it costs you 4 each run, meaning you only get two runs (with 2 left over).
1 bad pub: now it's only 3 per run, so you can hit R&D three times (with 1 extra)
2 bad pub: At 2 per run, you can hit R&D five times before needing more funding.
3 bad pub: Ten credits at 1 per run is ten runs.
4+ bad pub: Running is free, bro. Unlimited Keyhole-ing.
Do you see what happens there? Going from 2 per run to 1 per run doubles the number of runs you can make.
This is where Corporate Scandal is strong--when you are just piling on bad publicity and walking through ICE like it isn't there. Obviously, this is strongest out of Valencia--she starts with one bad pub, which turns on Investigative Journalism, and then between Frame Job+Fan Site and Corporate Scandal you can get yourself to 3-4 bad publicity without much effort. More than that if they're running Hostile Takeover or illicit ice like Grim.
Of course, you need to have a way to make productive runs. Trashing assets is a good start: remember that you can use bad pub money during runs on unprotected servers to trash those Museums and Mumba Temples and Pālanā Agroplexes. Hitting HQ repeatedly with a Lamprey installed can be mean. Keyhole as I mentioned above. Or get something with instant-speed installs like Self-modifying Code, Clone Chip, Personal Workshop, or Savoir-faire and use bad pub during runs as your personal bankroll. Why not?
Really, the greatest downside to this card is that you can only play one current at a time, which means you have to choose between this and Itinerant Protesters. Which is better: having 3 bad pub and forcing the corp down to two cards in hand, or having 4 bad pub? Depends on the board state and the matchup, I guess.
The point is, don't knock it until you try it. Valencia has many more tricks up her sleeve than just Blackmail.