If you're getting tape curls than something is definitely off on the tape path adjustments. Until you find whatever the tape is being trimmed by, you'll really have a hard time telling if the shed is related (which I'd figure it is) or is a different problem like with the tape itself.
Like Doc said, it's almost always a guide that is either out of adjustment or sometimes the inner corner will get a bit of something stuck in it forcing the tape toward the other side. These bits will snowball into larger bits sometimes. A severely worn head can do this too and if your machine has glass heads, those can chip instead of wear causing sharp spots.
But most likely, it's something out of adjustment. One reason it could seem like it's the tape is the other tapes that you've played regularly have already had their edges trimmed off. If the adjustment is off due to normal wear, this would've happened gradually to your tapes and until you played a tape that was "full width" you wouldn't notice.
I'd start by "getting in there" with a good light and a magnifier to look in those corners first, than any rolling part that might have slop in the bearing, and also tiny shinny lines polished by the edge of the tape.
Of course, there is the possibility that a batch of tapes got out of the factory with poor slitting but that's pretty unlikely. The Europeans used to point out their superior slitting to US tapes. The lack of outer flanges on even very large reels is pointed out some evidence of this.