There are, as you’re about to see, lots of problems with PGP. Fortunately, if you’re not morbidly curious, there’s a simple meta-problem with it: it was designed in the 1990s, before serious modern cryptography. No competent crypto engineer would design a system that looked like PGP today, nor tolerate most of its defects in any other design. Serious cryptographers have largely given up on PGP and don’t spend much time publishing on it anymore (with a notable exception). Well-understood problems in PGP have gone unaddressed for over a decade because of this.
The meta-problem with PGP is that it was designed by crypto-engineers in the 90s and it is horribly outdated, yet due to its federated architecture, difficult to update.