Funnest isn't wrong.
Best is already a superlative, and it's wrong to add the -est ending to make it
more superlative.
Fun is changed to the superlative by adding an 'n' and the -est ending, OR by saying
most fun.
Both forms are correct, though some people frown on
funnest.
On an interesting note, my wife says
more fun is correct (I say
funner), but she and I both agree that
funnest sounds just fine.