As an avid reptile keeper, (chameleons especially), I can tell you that ladybugs as well as 'lightning bugs' both contain toxins. How they react to your octos physiology is unknown to me, however, I would guess the toxins can not be good as food or water additives.
AH yes...the PA is the last bastion of "hot" reptiles...sigh. I wish we were a bit free-er out here on that subject...but, we can keep quite a few rattlesnakes. I used to have the nicest collection of tree vipers...
On the subject of the beetles... I wouldn't worry overmuch about one beetle being eaten, but I wouldn't push your luck...cover that tank! I think that spraying (the exterminator) would be worse than the beetles though...we stopped using toxins about 3 years ago...bought 6 banana geckos and just let them loose...works out great! (except for when we had to move...fast little buggers). Nary a cricket, scorpion, spider or roach shows its head for very long !
Pudge is still doing well although he still doesn't change colors like all the other octos that I hear about. I just finished covering the tank (again) with duct tape. We also have a bunch of boxelder bugs, are they as bad as the ladybugs?
We also have had an abundance of ladybugs in our area; so much so that several articles have appeared about locally. Not a day goes by that I don't hear my daughter screeching because the "ladybirds" are chasing her or the crunch of tiny shells meaning we've either stepped on one or my dogs have found a snack.
Don't have an octo (yet) but I've always read that animals have an instinct for items that may be poisonous to them.
For instance, berry's that birds don't eat, people shouldn't touch. My dog will eat almost anything, but grapes or chocolate she won't touch and these things are poisonous to dogs.
An octopus, with all it's sensitivity, wouldn't it know if something was ok or not to eat? I also wonder if they ever eat insects outside of captivity? I am so curious about these marvelous creatures. I can't wait to get one myself. Simply biding my time.
I once researched using crickets and other terrestrial arthropods as food for octopus and cuttlefish. Amazingly, crickets are taken readily by both young octos and cuttles. Of course, you have this little problem in the drastic difference in environments the prey and pedator come from.
Cephalopods are one of the oldest groups of animals that inhabit this earth- predating insects by about a gazillion years. Can a cephalopod gain any usable nutrition from an insect? It's hard to say- so little is known. I believe James Wood did a quick nutritional analysis of crickets and cockroaches, but I don't remember the results of that study.
As for instinctually knowing that ladybugs are toxic...I'd doubt it. When in all of evolutionary history have octopuses encountered ladybugs on a level that an evolutionary shift could occur?
I understand that most terrestrial predators find ladybugs taste bad. Octos are very big on tasting food before devouring it, so if cephalopods have similar tastes as finches, I'd bet the octopus spit it out. (somebody pilot a study on feeding fiddler crabs and crayfish to finches!!!! )
I'd just call it an accident and not worry about it. Far worse things have fallen in my octopus tank without incident- including an iguana.