I seldom buy older sets that are sealed unless the price is very reasonable or there is sufficient evidence to indicate that the boxes are in excellent condition, but I am probably more particular about condition than most are. Luckily, I haven't seen any insects or insect damage, but I have seen many of the other things you mention, Alex4420.
It sounds like you've been lucky with tape removal, but, if you want to avoid any damage or remaining adhesive residue, I would recommend applying heat while removing any tape (or stickers, like price stickers). This should be done carefully, of course, but it almost always works unless the adhesive is completely dried and hardened. I typically use a heat gun, but a hair drier could work too.
When buying used sets or parts, one of the things that bothers me the most is when the pieces have an unpleasant smell to them (usually from artificial air fresheners, cleaners, smoke, or pets). Often the smells can be cleaned away, but the softer Playmobil plastics (used for hair pieces, some capes or cloaks, and other parts) tend to retain smells even after thorough cleaning. If smells cannot be removed from a part, I refuse to put it with my other parts to avoid spreading the smell!
Good points! I hadn't considered the bug issue. Thankfully, I haven't come across it in Playmobil, although a used book I ordered some years ago had dead baby roaches in it. 
The seller was nonchalant about it.
That's unfortunate!
That would definitely bother me. I am very particular about my book collection as well!
With open sets, condition is a big issue, and it's not always obvious from photos. Ebay and other marketplace sellers are not meticulous like collectors when it comes to describing flaws. I've always known that most children aren't as, uh, neurotic, as I was, but getting back into Playmobil has shocked me with just how abusive some children are with their toys - and then to resell these toys without mentioning how mangled they are! I've definitely learned to be more cautious when buying used lots.
This is absolutely true. Many flaws cannot usually be seen in listing pictures. And, Ismene, you can be sure that there are at least a few others like you!
I think I’ve had the most problems with how sellers safeguard the items while they are shipped
I’ve bought thousands of sets and while in transit they get beaten up
I agree with this too; shipping damage is always a risk. I've actually had more issues with inadequate packaging and handling from large online retailers than individual sellers though. For new items, I try to buy from trusted sellers or companies that are known for their excellent packaging and handling standards; these sellers and companies almost always charge more than the others, but I find the additional cost to be worth it to maintain collector-quality condition.
I store PM in large plastic storage containers to prevent possible water/humidity damage and make them easy to move, but I can't imagine that is practical for thousands of sets.
If you too are sensitive to smells, you might want to be careful with selection of plastic containers. They can also transfer unpleasant smells to Playmobil parts (or other collectibles). This is especially true with cheaper plastic containers (and many of them also have problems with plasticiser degradation or migration or other chemical "off-gassing" or "out-gassing").
