There are some scary scenes, but nothing my own kids had an issue with. So it's going to depend on what your six year old can handle.
Here is what I remember (my kids love it too, so we have the box set of all 3, plus a separate copy of the fourth)..
First one: the scene where the ark is opened and there is chaos and swirling "forms". Also, being dropped into the pit with the snakes.
The 2nd: (Temple of Doom) has some very intense scenes where Indy and the boy are captured in the temple and there is a sacrifice. Cutting out of beating heart, type stuff.
The 3rd: (The Last Crusade) can't remember the scary part(s)? Maybe when the bad guy drinks from the wrong choice of cups/chalices and dissolves(?)...
The last: (The Crystal Skulls)--some creepy sci-fi stuff, but I don't remember anything really that bad-just action/adventure stuff: sword fighting, river rapids, shoot'em ups, etc..