The British Indian Army Riflemen use Lee-Enfield No. 4 Mk. Is. The No. 4 Mk. I was first issued in 1939, and formally adopted in 1941. They should instead be using the older SMLE No. 1 Mk. III.
Of note is because they are using blanks, which have no recoil, one rifleman is short-stroking his rifle. He is only drawing back the bolt 3/4 of the way before the brass breaks loose from the extractor claw, then tries to load a fresh round before he has expended the spent brass. This causes both rounds to jam in the chamber, and takes him several seconds to clear it by pulling back hard on the bolt.
When Indy and Short Round walk over the floor of bugs, Short Round refers to the crunching as "Walking on Fortune Cookies". Prior to WWII, fortune cookies were called fortune tea cakes, and largely only served in America.
The Ford Tri-Motor 4AT's instrument panel has an RMI, or radio-megnet indicator, and a VOR OBI, or omni bearing indicator. Both use radio beacons that were not invented until the '50s.
Indy manages to get the Shankara stones to turn red hot by uttering the incantation, "Tum Shiva ke vishwaas-ghati ho!", which is Hindi for, "You are a betrayer of Shiva." Considering that the stones are supposed to be ancient, any incantation that would make them do anything should be in Sanskrit, the ancient language of India, not Hindi, a language that reached its modern form in the late 18th and early 19th centuries.