Possible cause of harsh mids?

Once in a while you get that used album that sounds good except for a static like distortion on some more dynamic vocals, horns, guitar.  Just typical for some old albums?  Listening to Corea - The Leprechaun.  It's a very good sounding album, well balanced with great dynamics.  But, that annoying distortion rears its ugly head once in a while.  
I’ve gone through this for years, realigning cartridges more times than I can remember. All this to no avail, as it is the pressing as stated. Some older records were played on cheap a$$ players without antiskating, hence it is mostly heard in the left channel as the stylus was digging excessively into that groove wall. It sounds like sssss and often splashes into the left channel. It is annoying as hell, but short of tossing certain records, I just put up with it. I often just buy a replacement record, which often times solves the issue. There are also some poorly pressed brand new records that do this, however the ssssss and splashing is not necessarily in the left channel, just excessive sssss sound.
Classic Records Nora Jones come away with me had this issue on certain songs.
Yes Audioguy85, Back in the 80's commercial pressings were hit and miss but the static and other noise was not associated with peaks in the music. It was random. I had several Columbia discs that actually had little bubbles in the PVC with some of them open to the surface. There was a Warner album with something in the PVC, sounded like sand. I always took them back and got replacements. Sometimes the defect is in the stamper and you get exactly the same noise in every copy you get as the store usually gets a batch of consecutive discs off the same stamper. There was some great music on these labels and like you said, sometimes you just have to live with it....until you get a digital copy of the record:-)
One note on sibilance. Lowrider is right. It is unusual to get sibilance in a recording, it happens but it is rare. Sibilance, in my experience is a product of the system and or room. Sound between 3 and 4 kHz has a lot of energy and can bounce around a room for a relatively long period. Then our ears are more sensitive right at these frequencies, a perfect storm. If anything is prominent at these frequencies you will get sibilance particularly with female voices and violins both capable of broadcasting a lot of energy in this area. The BBC developed the Gundry Dip for this problem and many loudspeaker designers will intentionally cut a few dB out of this region to make their speakers sound smoother. My buddies Watt/Puppies do this. 
Thanks for the replies, gents.  Certainly only on a few albums so far.  Not sibilance per se, but more of a distortion on peaks in the mid band - guitars, keyboards, etc.  Bass and treble not an issue.  For example, another one that does it is an old Stanley Clarke album.  (Funny that it's Corea and Clarke!)  First song starts out with some drumming and bass for maybe 30 seconds and sounds good.  I'm thinking, good score for $4!  Then the guitar starts in and it's instant distortion. Grrrr

Brand new Rega P6 with exact cart.  I think I have it set up pretty well.  Most albums sound very good with no problems.  Other than the normal pops and ticks of course!  A definite upgrade from my old Dual.  I am leaning towards bad pressing or just plain worn out.  I am taking notes and will do a good cleaning asap.  Maybe that will help a bit.
pk, I just had another thought. The Exact cartridge has an extraordinarily high output, 7 mV! It may be overloading your phono stage. Here is the inexpensive way to figure it out and fix the problem. Go to Digi-Key and get a few of these, https://www.digikey.com/en/products/detail/stackpole-electronics-inc/RNF14FTD2R00/1974192
They are very high quality metal film resistors, 2 ohms. They will cut the voltage in 1/2 to 3.5. I would insert them right at the cartridge. Cut the resistor leads short, solder a cartridge clip to one lead solder the other lead to the red tonearm lead then cover the construct with red heat shrink. Do exactly the same to the white wire. The resistors are like 15 cents a piece!  If it does not work just return everything back to stock. If it works and sounds fine you have fixed the problem! If you decide to try this let us know what happens please. Another way to get an idea if this is the problem is take the record somewhere where you can hear it on another system and see if it distorts in exactly the same place. If it does then it is the record, if not then it is your system and the cartridge overloading the phono stage is an excellent candidate for the prize.