What is distortion due to?

Tough one. If it is more prominent in one channel than the other, then anti-skate needs to be adjusted. You did not say if you have a JMW-9 or Signature, but this is certainly the place to start. If all is well in anti-skate world, and I don't think that it is, you may need to increase tracking force to the top of the suggested range. Most MM cartridges put out between 3.5mv and 5.0mv, so with 2.5mv output from the Blacbird, you are certainly not overloading the phono stage.

I have been tracking at 2.0 gr, which is what is recommended.
It is a JMW 9, and the buzz is only on some records and is not just in one channel, so I doubt its anti skate.

I'll try a little more tracking force.

Could it be bad pressings?

First, it is probably a fairly serious problem, when the stylus loses contact with the groove wear is accelerated on both the cartridge and record. You say that it is not anti-skate, but have you put a twist in the wire from the tonearm to achieve anti-skate, and if so, how have you measured that the amount is correct? This is the trickiest arm to get anti-skate correct on, as it is so Mickey Mouse. I recently set-up a Dynavector XX-2 on a Super Scoutmaster and really had to monkey around until I got the anti-skate just right. Remember, if it is not correct, there is more force exerted on one wall of the groove than the other and side with less force will experience compromised tracking. My only other thought is are you measuring the tracking force in the plane of the record? Most scales require this, the exception is the, rather crude Shure balance, which is designed to work on top of the playing surface. And it could be bad pressings, but usually these make noise, but not buzzing, which would seem to indicate that the stylus is loseing groove contact. Are these the highly-modulated high-frequency passages that are problems?