Will having your middle initial on your ticket rather than middle name that is on your passport affect the use of global entry when coming into the US?
Since I stopped using my passport at Global Entry machines and began using a green card instead, the machines have (sometimes?) started asking me to confirm the flight I will be/was on against the record they apparently get from the airline, so they clearly have some interest in the flight. Since I still use the passport for check-in but use a different document at the machine, a guess might be that they don't ask about the flight when the document matches the flight record but may ask for confirmation when they don't and they found the flight record by a name/birthday match instead. Or something.
Regardless of the reason, however, it is the case that while I have a middle name in my passport I have never included that (full) name on a ticket; I have very occasionally ended up with my middle initial on a ticket when I paid with a credit card having that initial in the name. Neither the Global Entry machines nor anything else has ever cared, and when it has offered a flight record for confirmation it has always been mine.