Learn English – a woman who make a lot of fuss but does little or nothing called

ODO on have nothing on:

have (got) nothing on
informal

1. be not nearly as good as:
       bright though his three sons were, they had nothing on Sally
2. (have nothing or something on) know nothing (or something) discreditable or incriminating about:
       I am not worried—they’ve got nothing on me

The first sense is obviously the one to interpret the phrase as here, although it needs a bit of nuancing to match the context:

The Yankees aren't ready to comment on the specifics of this case, but there's nobody in the organization who would dispute the fact that Rodriguez now represents the worst investment they've made, 2009 title or no 2009 title. Carl Pavano for $40 million, A.J. Burnett for $82.5 million and Kei Igawa for $20 million have nothing on Rodriguez for $275 million.

The phrase "have nothing on Rodriguez" could be replaced with "have lost not nearly as much as Rodriguez".

In its straightforward "literal" sense, not for nothing is equivalent to for a very good reason.

But lately in the US it's used idiomatically (often followed by but) defined by UrbanDictionary as...

used to soften the blow of something that would normally be offensive or come on too strong.

There's also this Wordpress post giving the meaning “What I’m about to say is important” - which "sorta" makes sense as a "literal" usage (I have a good reason for saying what I'm about to say), though I must admit I've never come across it. But it can be seen as a "bridge" between the literal sense and the otherwise impenetrable idiomatic usage above (I have to tell you this because it's important that you should know it, but I don't want to tell you, because you won't like hearing it).