Simple, Hannibal never had a problem flying in planes. That was B.A. who didn't care for it.

The film pushes plausibility in other ways. Hannibal is on the FBI's most wanted list as well as Interpol's. They weren't able to find or catch him, but yet we're supposed to believe that a bunch of overweight peasant pig farmers were able to do so.
Yep, a notorious international fugitive gets a job as a curator in a major Italian institution where his photo will likely appear in newspapers and journals. (Kinda like that old
Star Trek
episode where the infamous war criminal tries to go incognito by becoming a Shakespearean actor and was surprised when Captain Kirk recognized him on stage.) Although I understand in the novel Lecter had plastic surgery to alter his appearance.

I totally agree about your issue with plausibility. On the other hand the pig farmers worked for Verger, same as key elements of the FBI. Clarice was given as bait and thus voil. It's not as though the Italians just showed up out of the blue then tracked down Hannibal. The OP's question about going through airport security is easily answered, Hannibal assumed the identity (credentials included) of someone else and though not particularly easy, it's also not that far fetched. As a side note, I would think it be more problematic buying an airline ticket without "help" (if on the lam) than getting through security.
He killed sixteen Czechoslovakians. Guy was an interior decorator.

The film pushes plausibility in other ways. Hannibal is on the FBI's most wanted list as well as Interpol's. They weren't able to find or catch him, but yet we're supposed to believe that a bunch of overweight peasant pig farmers were able to do so.

Happens all the time. Also, not everyone was looking for him. I don't think some TSA agent is on the look out. Heck, he got into the country and was on the FBI's most wanted list.
Seize the moment, 'cause tomorrow you might be dead.