EIDW - Ryanair can quite easily show an initial price on their website, then say it's a mistake and show you a new price, *as long as they have not taken any of your money* - they can put it down to a mistake occurring in their quote system which was automatically corrected before taking your money, which presumably happens on the websites of many other companies as well. It seems quite normal on travel websites to have a disclaimer saying that the fare quoted is not guaranteed until you pay either a deposit or the full amount. If they have not done so already, perhaps Ryanair could consider adding such a disclaimer ?
What is the exact Ryanair advertisement to which you refer ?
AFAIK, Ryanair have never claimed that their fares are *always* cheaper than the competition. They could likely back up a claim that for any given flight at some point they were selling it cheaper than competition. The slogan of "Low Fares" has a strong psychological meaning, but fairly weak specific legal enforceability.