These are what we call the 'YMMV items.' Things that some people find in this work. We call them 'your mileage might vary' because not everyone sees these things in the same way. This starts discussions in the trope lists, a thing we don't want. Please use the discussion page if you'd like to discuss any of these items.
Alas, Poor Scrappy: In Temple of Doom, Willie briefly has a near-moment, where she's almost sacrificed in a horrific way, by a brainwashed Indy no less. Unfortunately, after surviving it, she goes right back into Damsel Scrappy mode, and the audience's pity dissapears.
Rescued from the Scrappy Heap: However she manages to crawl out of that area twice, once during the mine cart chase scene one mook attempts to strangle Jones from behind. Willie (in a moment of inspiration) makes herself useful by punching said mook square in the face, sending him flying. She later helps Short Round prevent Mola Ram's escape by stepping on his hands (repeatedly) as he tried to climb pasted them.
Alternative Character Interpretation: Is Indy a true-blue hero? Is he a Blood Knight trying to break out of the humdrum existence of a university professor? Or is he a underdeveloped manchild trying to live out the adolescent fantasies of youth with a "secret identity"?
Most likely all three.
A good number of fans take Marcus Brody's deterioration in competence and death before the start of the fourth movie as evidence that he had a condition (say, Alzheimer's) chipping away at his cognitive abilities. Then there's the whole "once got lost in his own musuem" thing, and the fact that he only acts incompetent when out of his comfort zone (which never happened in the first movie). Indy fully expected him to get captured in the 3rd film, and admits he lied his ass off about how competent Marcus really was.
Americans Hate Tingle: Given Temple of Doom's portrayal of India, it comes as no surprise as to why it is not well received and was once banned in that country. To a lesser extent, many Russians had similar feelings in regard to Kingdom of the Crystal Skull.
Angst? What Angst?: In The Last Crusade, Elsa is severely traumatized, screaming her head off, as Donovan dies right in front of her eyes, from something she deliberately did to him no less, and yet in the next scene she acts as if nothing happened.
Kingdom Of The Crystal Skull. Some people say it is total crap, others say it was fun but not up to Indiana Jones standards, some liked the acting and characters but not the writing, some liked it all except for the Gainax Ending, Shia LaBeouf blames himself and his monkey-swinging Tarzan act, and then there are those that hold it as being better than Temple of Doom but not up to the standards of the "Nazi" movies. Really, it isn't broken so much as shattered into thousands of pieces.
Temple of Doom gets this, too. It mostly comes down to whether Kate Capshaw was too annoying for the movie to be enjoyable.
It also comes down to whether the Gorn was too much.
Unless it's The Last Crusade, because of the quest for the Grail and Sean Connery as Henry Jones Sr. But having said that, Crusade is the most well-remembered of the sequels largely because of its faithfulness in tone to the original.
The "no ticket" scene is much funnier now that something similar happened in 2011. It counts double when you realize that Indy tried to pass himself as a Scottish Lord earlier in the film. "How dare he?"
Special Effect Failure: Prevented by, of all people, the MPAA in Raiders. The model of Belloq's head which explodes during the film's climax can be seen in the behind-the-scenes footage of the DVD, and was laughably unconvincing. However, the MPAA objected to the blood and brain fragments that could be seen after the explosion, and so the film makers obscured the sequence by superimposing flames over the footage... which had the side-effect of covering up the model's deficiencies and making the scene look pretty convincing!