Throwing everything else aside. I have one simple question. Oswald kills Kennedy and gets completely away free and is safely ensconced in his rooming house several miles away from the scene of the crime. So what does he do? Leaves the safety of the rooming house, supposedly murders Officer Tippit and then after doing that continues on back downtown towards the scene of the initial crime and gets busted because he walks into a movie theater without paying.
Does that make any sense to you?
There's a lot about the Tippit killing that doesn't add up. It may be sloppy paperwork, but to this day (despite some saying the matter has been resolved) there remains a lot of murkiness surrounding Oswald's wallet(s). Reportedly an unknown witness to the Tippit killing "found" Oswald's wallet near the scene and gave it to police. This "find" was critical because that wallet also had ID for "A. Hidell" which linked Oswald to the purchase of the Carcano under a pseudonym. Yet...some Dallas PD (DPD) paperwork indicates that at the theater arrest scene, Oswald was identified by ID in his wallet taken from his pocket.
At the time of the assassination, DPD was notably rough and corrupt and some "Oswald as patsy," theorists suspect Tippit was murdered in the belief that DPD would not let a cop killer survive being arrested, neatly concluding the events of the day. As Oswald was in a theater full of witnesses, the DPD was not able to administer street justice and Ruby had to come bat clean up a few days later.
I can possibly see Oswald's wallet being left at the scene...i.e. an officer stops somebody and asks for ID, the subject removes his wallet and then a scuffle ensues. What I find more troubling is that police "recovered" four expended .38 caliber shell cases from the Tippit murder scene. I can not envision any circumstances under which Oswald, having just shot an officer and wanting to flee the scene, would have stood there and emptied the cylinder of his revolver before leaving the area...and if he took the time to do so, why he wouldn't have also collected his wallet.
Sounds to me like somebody who hadn’t thought out their plan beyond “doing the deed”. They were having conflicting ideas of what to do next.
Shades of the scene from “Julius Caesar”, where the assassins have finished knifing Caesar, and are standing around debating whether to get out of Rome before they’re found out, or hold up their bloody knives before the populace with pride.