@bubu,
Quote:1. a famously inaccurate headline.
2. a famous inaccurate headline.
Is there any difference between these sentences?
Yes.
In 1., "famously" modifies "inaccurate",
and in 2., "famous" qualifies "headline".
And 2. is not very good style, imho, although the meaning is not unclear.
You yourself have noted that the second sentence needs something else.