Is there any crime the three wise monkeys (who see no evil, hear no evil, and speak no evil) could collectively "witness" and not be able to indict the suspect?
Clearly it depends on your definition of "evil" - the third monkey, whose sight and hearing are not restricted in any way, is a perfectly good witness who could identify the culprit easily enough. Were you to declare that saying "It was John who robbed the bank / shot that guy / lit the fuse" was somehow speaking evil, then I could declare that one of the other monkeys who had only partial information could (suggest to a cop/prosecutor to) ask questions like "who was that running away afterwards?" while testifying what they saw or heard the running away guy do while somehow not being sure who it was.
So I say no, I can't think of any witnessable crime that the three of them can't testify succesfully about.
It depends on how much freedom the monkey who can "speak no evil" has. Does this mean that he can write? Sign language? If so, then he effectively has no limitations since he can communicate fully. Thus, there is no crime (apart from the monkeys being killed like in a previous answer) that he cannot indict.
If he cannot do these things, then he cannot communicate at all and goes from the most useful to the least useful of the three monkeys; in fact he is completely useless since no matter what he witnesses, he has no ability to communicate it.
Thus, you have the other two monkeys, one blind and the other deaf.
If the crime involves both senses to decode, then it would not be fully understood by either. However, if the monkeys could communicate some how and share their experiences, then they could potentially figure out anything. So lets assume they are unable to communicate.
A simple example of something neither would be able to understand on their own, but together they would, would be a visible code and an audible key. The deaf monkey would see the code, but not be able to decipher it, while the blind monkey would hear the key, but not have nothing to decode.
Two men walk into a bank, wearing masks that disguise their identities. One of them speaks, his voice clearly identifying him as John Wayne. One of them shoots the teller and takes the money. Both leave. There are no cameras or witnesses other than the monkeys.
Blind monkey knows that one of the two men was John Wayne, but doesn't know whether he was the shooter or not.
Deaf monkey knows which man shot the teller, but didn't hear them speak, so he doesn't know which was John Wayne.
Mute monkey saw and heard and knows whether it was John Wayne that shot the teller, but cannot communicate what he witnessed.
The 3 wise monkeys are having dinner.
On the next table sit 3 very attactive monkeys so every move is attentively watched. We will assume they have different wigs on that stay in place and are not particularly wise so we can distinguish the 6 monkeys.
The brunette monkey complains that her banana daquari is not sweet enough and that she has to go to the bathroom. She stands up, the blonde follows, and the redhead says "I'll catch up I need to check my email". (Ok they are smarter than normal monkeys.) After finishing with her phone, the redhead takes a container labelled "agave nectar" from her purse and puts some in the brunette's drink. She then goes to the bathroom. After a couple of minutes, the blonde comes back. She takes a contain labelled "monk fruit extract" from her purse and puts some in the same drink. The other monkeys come back sit down and the brunette takes another sip. "Hm," she says, "That is much better. But why does it smell like almonds now?" She then collapses on the ground dead.
No observer could have figured out who did it unless they, after the fact, search the friends.
There are a couple of loopholes in the question.
If you were to kidnap the 3 wise monkeys, they would all witness it, but none would be able to indict you.
Similarly, anything which adds disabilities to the monkeys, ie. making them all blind. Again, they can all witness it, but assuming you take care to protect your identity (wear a mask, talk in a chipmunk voice), none can ID you.
Last one I've got is that if the suspect is actually not the criminal, then (assuming the monkeys are lawful) they wouldn't be able to indict the suspect - the question doesn't say indict the criminal.