Quite a few processors have some undefined behavior, some instructions flags are just not specified, and no not just "this is reserved and must be zero", that would be Ok.
The result of the `bsf` or `bsr` instructions on the 0 value
And please, don't look too much at the FPU either or it may do some random stuff and jump at you.
But CPU architectures also have undefined behavior. ARM for example calls these "UNPREDICTABLE" and "CONSTRAINED UNPREDICTABLE". Have a at the Armv8 architecture reference and grep for those. Lot's of ways to write programs in pure assembly with undefined behavior too!
x86, 6502 and Z80 etc all have undefined / unpredictable behavior too.
EDIT: Thanks to IcePic's answer, I found it here: https://web.archive.org/web/20210405071521/http://visual6502...
And for the last part of your sentence, it depends on what address you run some of the instructions from, since they take a byte out of that in account when doing the weird operations, so some bad instructions can be used, if you are running from $fe00 - $feff because it takes the high byte ($fe), adds one to it, then ands something else with it and lastly produces a result that leads to a usable instruction, but only if the and is with $FF so it doesn't drop bits on you. =)
Lots of weird/fun reading there.
It's a shame that I cannot find the other article, because I remember that the author actually had looked at the individual transistors, and figured out the bus conflict or whatever it was, which pretty exactly described what happened, and maybe even why some bits would be more "weak" than others.
EDIT: Oh, hah! Your PDF actually links to it in the same section. The wiki seems currently down, but here's an archive.org link of the page that describes the unstable opcode in great detail. So thanks a lot! https://web.archive.org/web/20210405071521/http://visual6502...