I have a contact with no contact details, apart from a name and which can't be deleted. The option just doesn't appear in the context menu like for other contacts. Is it possible to delete this contact?
Try deleting it from your Google contacts. If it's not in your Google contacts, it probably came from another source, like Facebook or Twitter. You should also be able to hide contacts that don't have a phone number, so as a last ditch effort, that may be good enough for you.