No te hagas el bobo = Don't act like a fool
No te me hagas el bobo = Don't act like a fool (but it has a different emphasis that is impossible to explain)
Could anyone please explain the differences?
The "me" in "no te me hagas el bobo" is a solidarity pronoun. It's used to create a stronger link between the speaker and the audience. This is a topic that has been studied in sociolinguistics (google "solidarity pronoun"), and some languages such as Galician and Basque (as far as I know) have special constructs to express it.
Basically, "no te hagas el bobo" and "no te me hagas el bobo" have the same meaning, but the latter adds the solidarity pronoun "me", which links the action of the doer ("hacerse el bobo" in this case) back towards the speaker, thus strengthening the emotional connection between both.
The translation of "no te hagas el bobo" is "don't play fool"; the translation of "no te me hagas el bobo" would be something like "don't play fool to me". That "to me" bit marks the solidarity connection I am describing.
I think that the "solidarity dative" is perhaps known better as the "ethic[al] dative," about which you can find a lot with a Google search. It was very common in Greek and Latin, and is still used in modern languages, such as, obviously, Spanish. Although we do not think of it as something we use in English, the Wikipedia article on the dative gives a good example: "Cry me a river."