As reported by Screen Junkies and a few other sources, the TIE fighter was just inserted into already shot footage of Jyn walking across the platform. Apparently, the trailer company added it themselves, and Lucasfilm liked the result enough that ILM was asked to refine it. I find this relatively believable, considering the same angle is used sans TIE fighter in the finished film.

Also heard from a fairly reliable source (not online) that the first Vader scene (with him standing in front of the monitors) and Krennic talking about immeasurable power is nothing more than the original version of the Bast Castle sequence. The original Vader actor apparently didn’t move quite right, hence why there are two actors credited.

From this information, the official narrative, which may very well be true, is that the most affected sequences by reshoots were:

The beginning with the added introductory sequences to Jyn, Cassian, and Bohdi; it originally cut from the flashback to the briefing sequence, which, as per the original teaser, had more explicit verbal exposition of Jyn’s character which became redundant when she was given an action-packed introduction. K2-SO was also introduced further down the line, as seen in an early trailer: “The Captain says you are a friend.”
Saw’s stuff was retooled with Saw now having a different appearance. This was because Jyn’s character arc may have been changed in reshoots (more on that down below). Note how his prevailing message in the teaser is negative towards Jyn pursuing rebellion: “What will you become if you continue to fight?” instead of the completely opposite positive message in the finished film actually encouraging Jyn to join the rebellion’s cause: “Save the rebellion. Save the dream.” Bor Gullet was originally used to explore Jyn’s background/past, not Bohdi’s.
The heist of the Death Star plans was heavily truncated in order to avoid bloating the third act when the space battle was heavily expanded. This included such simplifications as making the archive and the transmitter in the same building on Jedha. You can see the original transmitter building (to where the crew was running) in some shots in the trailer. Most definitely reshot was the confrontation between Jyn and Krennic (possibly happened on the beach originally); the effects get ropey enough that it seems they were composited in.

This all does not discount alternate shots, also confirmed by the official narrative (particularly Ben Mendhelson’s interview about lots of alternate takes), which can be chalked up to Gareth Edward’s knack for experimentation. They’d play a scene radically different ways (eg. Krennic pulling a blaster to Tarkin’s face) and pick the best result.

(SPECULATION) Jyn’s Character Arc

As alluded to above, I personally suspect that the reshoots were predominantly done to make Jyn’s character arc more consistent.

In the finished film, Jyn transforms from the adamantly neutral party (“You can stand to see the Imperial flag everywhere?”/ Jyn: “Not a problem if you don’t look up.”) to a full fledged hero, who sacrifices herself for the cause of the rebellion. It’s a well-worn but undeniably effective character arc, not unlike that shown in a movie like Casablanca (minus the literal sacrifice bit). Crucial to altering this arc was the addition of the scene with the “look up” line above, as well as completely retooling Saw’s relationship with her by reshooting the Jedha scenes between the two to change Saw’s message to “Save the rebellion. Save the dream.”

I propose that in the original cut of the film, Jyn transformed from an anti-Imperial violent lone loose cannon (not unlike Saw) to a team leader. This is substantiated by Felicity Jone’s early promotional description of her character as someone who wants nothing more than to “bash stormtroopers’ heads in,” a characterization not quite apparent in the final film.

Indeed, Cassian was changed as a result; originally described as a recruiter (again, not in the final film), he was likely the one who saw the potential in her, trusting her enough (as seen in an early trailer) to help pilot the ship to Jedha and support her during the briefing. Saw’s part would be to convince her character that she needed, unlike him, to use less extreme methods, lest she follow in his footsteps (which leads to alienation and bodily damage).

The final point to understanding the original arc and perhaps the key reason that it proved ineffective dramatically is knowledge of the shooting screenplay’s happy ending. It seems a natural conclusion that if Jyn’s arc was to become a leader; she would be “rewarded” by film’s end with a position in the rebellion. That being said, because Edwards was given permission for all the characters to sacrifice themselves, it no longer satisfyingly concluded her arc. They shifted the arc in reshoots to better fit the ending (which they realized was one of the most potent parts of the whole film).