Есть и много других значений/оттенков:
http://context.reverso.net/перевод/русский-английский/палец+в+рот+не+клади

http://enc-dic.com/phrase/Palec-v-rot-ne-kladi-971.html

Refers to someone who can stand up for himself. One should be careful when dealing with that person as he/she can take advantage of someone's gullibility. That kind of person is usually well-spoken, sneaky and enterprising.

ему палец в рот не клади - может откусить по локоть

Alexander, did you write that yourself?

That's a well-known saying.

Grumbler, thank you for the links!

Did you write that explanation yourself?

That simply means something like - don't treat this guy lightly as he is not a weakling as he seems to be.

Yep

Your English is very impressive, young man.

So I guess it means something between "don't underestimate him" and "don't trust him as far as you can throw him"?

I'm wondering what "you can throw him" would mean?

It’s an idiom: imagine if you could pick Alexander up and throw him, how far would he go. Not too far, huh? That’s how far you trust him 😅

Не совсем переварила это, но don't umderestimate him мне сразу показался - не в бровь, а в глаз. ;)

Я верю ему настолько, насколько я могу его бросить. (буквально)

Значит, что я не очень ему верю.

Если бы я был сильным и большим, а он слабаком, я бы легко мог его уделать, поэтому я бы ему доверял.