Indeed ignore it, it won't show up on the gate mini screen anyway. If someone does notice it then they can fix it the airport if it's within 3 letters. Best not to use middle names, it just adds to the unnecessary points of failure and isn't required. Advance Passenger Information - if applicable for your destination - is best matched up but all the systems I'm familiar with do a Primary Key on the passport number and Secondary Key on the date of birth.

There is a 24 hour period when tickets can be refunded or amended without fee, that's the time to check these things.