Not sure if anyone did anything wrong other than mishearing. A passenger thinks she hears someone sign off of a conversation with "martyr" and reports it. Given that information he's thrown off the plane which is also reasonable.
The guy who got kicked off also did nothing wrong. He was just talking to his uncle.
I suspect the same thing would happen to anyone regardless of race or nationality should the words Allah and martyr be uttered in close succession on a plane.
So no. Many people did lots of things wrong that day. The passenger who obviously doesn't know arabic mishears a word and reports him out of prejudice. The staff who took the complaint seriously because of his race. The security and FBI who harassed him for a long time as a result.
Do you really think a white man uttering Allah (where that's the only word heard by another passenger) would be subjected to the same treatment? And also, even if the man WAS a terrorist, do you really think he would go on the phone and talk about his terrorist plots in the open? Even if this guy said "martyr", that still does not warrant the treatment he received. Just like if Bob actually said "suicide," literally it's just a word that's sometimes used in a bad context. He wasn't misheard as saying "I will blow up this plane." So it took many layers of prejudice for this to happen.
Southwest should have also removed the reporting woman from the plane so the victim could face his accuser, and also to reduce frivolous complaints. If she really thinks he was a t'rist, she should be wanting to get off that plane regardless.
It seems reasonable, and incentive-aligning, for both of them to be removed from the plane.
So a ban on saying the word "Allah" is basically a ban on speaking any normal variant of Arabic.
"inshallah" (God willing): Hopefully
"al-hamdu lillah" (praise the Lord!): Fortunately
"wallah" (oh God, wow): I swear, I promise
etc.