Our intrepid heroes are in a dungeon, when they enounter a giant alien blob from the Outer Planes, something they've never seen before. The player clicks to examine the blob and discovers "Ahah! It's only a moderate threat!"
Tell me again how the heroes knew a giant blob from another plane was only a moderate threat? The accuracy of the CR information is a situation where there can be a lot of work can done. Getting the CR info could include some familiarity/skill checking.
Our heroes are probably able to make a fair gauge of the threat of creatures that are similar to them, but probably less so for alien blobs. So one aspect of the difficulty of getting accurate CR information should be the similarity of the monster to the player racial type, outsiders are going to be difficult to determine if the party is human/elven etc, humanoid monsters our heroes would likely have less difficulty with, and plain old humans the heroes should be pretty accurate on for this aspect.
Skills can play an aspect here as well. Spot, survival would be pretty obvious. Maybe spellcraft for more exotic creatures where it might be relevant (nishruu, monsters that can be summoned). Craft alchemy ("Hmmm, that smells like a terrible acid!"). A lot of skills could grant insight into different types of creatures.
I could see a system where the player can get multiple levels of information about a monster's CR when they click examine the monster.
None: the creature is too strange for the hero to make a determination.
Some: "dangerous/non dangerous". The hero is able to make a determination, but it may not be that accurate.
Normal: As it works now ingame.