An incorrectly spelt middle name is not going to cause you any problems whatsoever.
I booked flights with Emirates to Bangkok through Expedia, but due to their site being down at the time, I had to book by telephone, relying on somebody else to correctly enter my details. Instead of putting my first name as 'Michael', they entered the it as 'Micheal'. Not the end of the world, but it was incorrectly spelt!
A quick call to the airline confirmed that there would no problems.
Have a great time in Budapest. I went 4 years ago and had a brilliant tiem.