Joe Thornton is an easy answer here. If I'm remembering this correctly, he appeared in 33 playoff series and he led ZERO of them in scoring. This is a guy who in his day was a regular Art Ross contender. Won the Hart.
But I'll also mention Keith Tkachuk. He may yet make the Hall of Fame, and probably should. A multiple 50-goal scorer and regular 40-goal type of player. Though they were short runs, three of his first four playoffs (two Winnipeg, one Phoenix) were actually quite productive. But, after that, when he was very much in his prime, he had 14 goals in 63 playoff games, which is bad.
(It's probably not fair to even mention him because he appeared in only 25 playoff games, but Dan Cloutier was brutal. In his 25 appearances, his stats show 27 goals against him above average. The thing is, though, nobody ever really thought he was anything special... except for Marc Crawford.)
Alex Mogilny was pretty poor, too, for large stretches of his playoff career (4 goals in 23 games when the Devils won the Cup). But he had some good years, too, so he doesn't really merit mention, I guess.
It's hard to say with Marcel Dionne. His numbers are mostly quite poor (esp. if you delete 1982, which was a fluky / weird playoff when the Kings upset Edmonton), but his teams were usually quite bad and overwhelmed in the first round, with atrocious goaltending. But, you know, if Steve Yzerman had had a career-ending injury in about 1995, we'd also be looking back at his playoff resume as similar to Dionne's. Sometimes, it's all about team context.