He doesn't enter, but just stands there just outside the door and keeps his back turned to the street. Brewer notices that TM is staring (as you like to point out), but he's not staring at the merchandise in the store or the display cases on either side of the vestibule.
How would Brewer know what the man was looking at?
The police cars make a U-turn at Zang, half a block short of reaching the shoe store, and head back to the East. TM looks over his shoulder, then proceeds in a Westerly direction, away from where the police cars came from.
"Avoiding the police" is just injecting a biased assumption based on what you already believe. Maybe he was looking over his shoulder to avoid knocking down another pedestrian who might be walking by. If the police cars turned around at Zang, why would he need to look for police cars?
TM continues on until he reaches the Texas Theatre, when Brewer sees TM disappear into the recess at the front of the theater. Brewer walks to the theater, doesn't see the guy reappear, and notices TM isn't in front of the theater when Brewer gets there.
You forgot the part where he went back to the shoe store first.
Brewer realizes that TM had to have entered the theater, and asks the ticket clerk whether she'd sold TM a ticket. He gets a negative response;
No, she said she wasn't sure whether he did or not.
the guy snuck in. You might be the only sucker alive who couldn't see that as suspicious and evasive behavior.
Be honest -- you consider it suspicious behavior because you already believe it was Oswald and he was avoiding the police.
He was arrested after he struck a policeman and pulled a gun. Let me guess: you don't consider that suspicious behavior, either.
Actually I consider that a false statement. McDonald didn't say he pulled a gun. Besides, he was arrested for murder, not for striking a policeman or pulling a gun.
The criminal trespass thing would in itself have created probable cause to arrest and search Oswald once Brewer pointed him out.
No, actually it would not have been. They had no probable cause for criminal trespass either. And they tried to search him
before they arrested him. No go.