Why were some shots in LC mirrored?

This always irritated me
In the opening scenes of LC like when Young Indy transitions to Older Indy when Fedora puts the Fedora on his head.. some of the shots are mirrored
You can tell because the blood switches places, the ribbon on the fedora switches and the fat guy in stripes holding Indy switches places

Likely because they filmed it from the wrong angle and only realized it in post, and flipped the image in editing.

They did this in TOD too when Indy was under the spell of the blood and then Short Round burns him to get him out of it. When he hugs him and turns to Willie you can see the scar on his chin and his part in his hair are on the opposite side.

It happens a few times in Young Indy, too, but a big shot in "Raiders" is flipped. The last, long shot of Indy's mad dash through the digsite crowd on horseback
is reversed as you can see his bag on his right side instead of the usual left. It appears to have been done to match all the other stunt riding bits. Notice how
Ford intentionally wears the bag on his right in the closer shots (coming out of the tent on horse & at the top of slope) but the hat's ribbon is the proper place.
Only the top shot of Terry Leonard looking down onto the convoy has the bag on the left side.

You can tell the digsite shot is flipped because the Opel Olympia in the background has its spare tire on the wrong side and most of the soldiers look left-handed
by the way they carry their rifles. Part of the correct version can be seen in the teaser trailer.

Stuff like this isn't bothersome but is fun to point out. I never noticed the one in "Doom", sandiego!

You never noticed that? The "Right! All of us!"-Scene is probably the famoust mirrored shot. It's very-very easy to recognize mirrored-scenes with Harrison Ford because you can see it at his nose. The are mirrored shots in many Ford-Films... Jedi, 6 Days, 7 Nights and so on...

About mirrored shots in Temple:

"There's one funny thing," Kahn says. "on the second Indy, almost every other couple of cuts, George would say 'I wanna flop this (reverse the direction of the shot) - I want it the other way'. He made alot of flop shots. So my assistant and I got him a cap that said Professor of Flopology. And we put the letters backward, too, so you could read it in the mirror, He laughed when I gave it to him.§


Source: The complete making of, page 173

Maybe they mirrored that scene in TOD because they cut the scene of Chattar Lal's death.