Technically, everybody takes a singular verb. Try replacing it with "every single body" or "every person".
The main ambiquity in the phrase is that 'their' isn't -technically- correct as a gender neutral third person possessive pronoun, despite its common usage in that form. (Say -that- five times fast!) If you replace 'their' with 'his or her', the agreement makes much more sense:
And you can get wonderfully creative with something like
"The group changed its mind"
and
"The group changed their minds"
depending on the meaning you want the statement to have. Are you emphasizing the concept of "group-think" or the independent conclusions of the individuals?
It's more poetic than
"The members of the group changed their minds".
or
"Each group member changed his or her mind".
But at least you get a ridiculous bag of options for a single sentence.
The main ambiquity in the phrase is that 'their' isn't -technically- correct as a gender neutral third person possessive pronoun, despite its common usage in that form. (Say -that- five times fast!) If you replace 'their' with 'his or her', the agreement makes much more sense:
Personally, I would just rewrite it completely: English is fun!