For me the main one of those is the assumption that fairytales are twee little stories for young kids and I have come across that view. It tells me something about the person holding the view immediately - they haven't read the original tales, they've only seen Disney at best! (And that's not to denigrate Disney at all - there are, within its limits given its audience, grim bits - for example the murder of Simba's father in The Lion King. I'm fond of many of the Disney versions and accept the fact they simply could not have made The Little Mermaid the way Hans Christen Andersen wrote it).
The other challenge is that fairytales often carry a strong moral message but do so in an entertaining way and without being preachy. Often the message is not spelled out directly, you pick it up from what happens to the good and bad characters. Often fairytales have many layers to them. Just how many layers do my stories have? Fairytales are not 2D so the challenge is to ensure mine are not either.