I never put my middle name on my bookings. Some of my IDs have it, some don't. I've never had a problem with any of them. I believe you do have a middle initial field in the TSA secure passenger data you can enter (along with your gender and DOB).

BUT, most of my travel is domestic, so int'l might be another wrinkle. Probably worth a call to DL to either get the PNR fixed up or, if all is well, put your mind at ease.