Does improper alignment cause permament damage ?

From what I learned from various sources in the industry, yes. Poor tracking bad enough to cause a lot of distortion sounds like something that should be addressed.Since you listen to these records they must have enjoyable value.The stylus and record both will suffer from extra wear.A damaged stylus will ruin a record also.I would want to correct the problem since it may not be to late.I hope you caught it in time.

As Elizabeth says, it depends.

1. Does this distortion happen in synch with dynamic peaks in the music or is it more random?

2. Can you describe how it sounds?

The thing that does the most damage to record grooves is cartridge mistracking. When a stylus is simply incapable of following the groove modulations, it exerts contact pressures hundreds of times higher than when tracking an unmodulated groove. The fact that a lousy cartridge may require 5gm of force to eliminate most mistracking is what gave rise to the idea that it was the high tracking force that ruined discs. It is, rather, the stylus's inability to stay with the grooves at any reasonable force that does the damage. With a cartridge that tracks fairly cleanly at up to 2gm, you should expect several hundred plays before a highly modulated disc is ready for the dustbin.

From Stereophile [http://www.stereophile.com/reference/170/index7.html]