Checked my copy of AVP which I bought within a week of it's street date a few years ago and it still plays fine. menus, scenes, ect - no problems. In fact, I was surprised to be reminded how fast the movie or chapters load and play when selected in the menu unlike most titles these days.
Regarding laser rot, I'm sure there will be incidents reported concerning specific titles as time goes on and more titles are available. I remember back in the early days of laserdiscs, I had the first release (full screen) of "Greystoke: The Legend of Tarzan" and after about a year, I went to play the movie and noticed copper/brass colored "speckles" all over one side of one of the two discs and it wouldn't play. This introduced me to laser rot and as many laserdisc collectors know, late in the format's history in the mid/late 90's many titles from Sony/Tri Star including "Starship Troopers" and "Contact" from a certain factory were prone to laser rot due to contaminants in the chemicals and process used to bond the plastic clear layers to the metallic data disc. Entire runs of these titles quickly rotted and became unplayable within a few month's time.
Laser rot has been noted in certain titles produced on dvd through the 90's as well. "Kentucky Fried Movie" and certain Anchor Bay Hammer Horror dvds were prone to rot and become unplayable for instance.
Laser rot doesn't always manifest itself as physical discoloration on a disc. Usually it will show as either speckles as noted on the LD example I mention but it can also show as a coppery or gold colored discoloration on the entire data side surface of the disc that grows more pronounced over time. This is usually due to excess moisture/ high humidity contaminating the laminating process causing the thin metallic data disc to actually "rust" over time. Sometimes it can show as a sort of "clouding" like the plastic or acrylic resin laminate begins to outgas or break down, usually due to improper mix or contamination of the chemicals to make the layers at the manufacturers plant. However, there can be no outward visual signs the disc is going bad until the day you try to play it and it fails to load.
As the process to manufacture consumer discs has evolved in 30+ years, such problems have been addressed only to have different issues with similar negative results occur. But the instances of such problems has greatly been reduced over time.
I've run into laser rot in every type of data disc at some point. CDs, DVDs, LDs.... I have yet to find laser rot on a Blu-ray title (I have about 300 titles so far) but I'm sure I'll run into it sooner or later.