This is a really tough question because the downbeats of the movie are right around the middle for me. I'll try to break it down to explain.
1) Club Obi Wan
Actually a pretty good sequence for the most part. Wan's death should have had more meaning in the final film (the reaction of Short Round to hearing the news was cut). It serves to introduce us to the two new characters in their 'comfortable' surroundings before Indy (somewhat accidentally) wisks them away.
2) Nepalese Plane Ride
For me, this is a bad sequence, with some painful character moments, the first of Willie's whining and 'noise', and a series of over-the-top-stupid stunts that completely break suspension of disbelief. It's also the most light-hearted action sequence we get, which ill-prepares you for what's coming down the road.
3) First Exposition
We meet the plot here and this is also where things really start to go awry. We get told (not shown) about the Sankara stones, and that the kids are missing. The drama and tension of this bit is undermined by the 'comedic' antics of Willie again and it's easy to miss what's going on. This ends with the lone escapee from Pankot, which should have been a far more poignant scene than it was.
4) Trip to Pankot
More Willie and Short Round antics as we make our way to Pankot. This sequence seems a bit more oddly-placed as it's like we're supposed to have some 'mood-lightener' after the Exposition's last scene, yet we get Willie at her worst here, a little more exposition on Sankara, and some forced gags. It's this sequence that ruins Willie's character... the only saving grace of it is the end, where Indiana finds the altars and warns Shorty around. There's danger ahead.
5) Dinner at the Palace
Until the infamous Fridge, this was the worst scene in all of Indiana Jones. People have gone at length about how racially insensitive it is (and it most certainly is that), but the worst part is that all the attention is put onto Willie and Short Round's antics at dinner. Meanwhile there's an extremely important conversation between Chatter Lal and Indiana Jones that the movie is so distracted from that most people miss it even on repeated viewings!
6) Romantic Evening Gone Awry
This is really one scene, but it's one of the few were Willie's original characterization shows up (angry and playful with Indiana) and one of the few where there's some actual chemistry going on - amusingly when they're angry with one-another!
7) Trip to the Altar
Finally, back to some Indiana-style action! Well, mostly. We get a fairly good sequence here of the traps and secret passages of Pankot which eventually leads to watching the sacrifice. Willie is again played up for laughs but is more subdued than before. Short Round also seems to fall into place as the 'heroic sidekick'. Indiana, though, falls short as he goes for the Sankara without thinking anything through.
8) Captured by the Thugee
If you ever felt like something was missing between the last bit and this one, you're not alone. Some very neccessary establishing scenes take place here, with Willie sending warning to Captain Blumbertt, discovering Chatter Lal's true alliegence, and so on. Instead of that we get a very long sequence of drugged-out Indy and captured Short Round. We're also introduced to Mola Ram without any foreshadowing whatsoever... fortunately the man has presence and establishes himself as a villian pretty damn fast.
Sadly, though, this is where most people throw up their hands at the movie and decided Romancing the Stone was more fun. The movie could have worked a lot better with less of Indy's really bad LSD trip and more of the needed establishing scenes. The sequence ends when Shorty brings Indiana Jones around and we get...
9) Fight at the Altar
From this point on, the movie is actually good. The altar fight is the first in several tight action sequences. Indiana battles Chatter Lal, a bunch of Thugee, and Mola Ram promptly escapes in another secret tunnel. Victorious, Indiana Jones is set to leave with the Sankara stone when he hears the cries of the captured children (remember them?)
10) Freeing the Children
Another series of good fights between, well, nearly everyone. Willie's out of her element here, but damn if she's not totally psyched to have Indiana and Shorty beat the **** out of a bunch of thuggee. To be fair, Willie actually does a lot of saving of children while the boys are occupied. Other than a couple of awkward shots, this is what people spent their $5 to see.
11 ) The Mine Cart
Children safe, time to get the hell out of here. Oddly, this is a little hard to reconsile as to why Indiana and company go in a different direction than the kids they just saved. This is explained in the novel and comic, but whatever... let's roll with it (pardon the pun). The cart chase is a very fun, if gratuitous, action sequence which primarily serves to take us from Pankot to the finale. It's the sequence everyone thinks of when thinking of this movie, but it ends with a very bad effects shot on the cliff when the water bursts out of the tunnel.
12 ) The Bridge
Easily the best part of the movie. There's tension and a real sense of danger here with Indiana Jones in a craptacular situation. Poor Willie's probably had her fill of everything by this point, and her brief moment of smugness is erased hard by Mola Rom's 'screw you' attitude. Fortunately, he doesn't recognize that Indiana is bat-**** insane and that lack of foresight causes him to become alligator chow.
The scene fails a bit only because the needed scene for Blumbertt's warning was cut from earlier. Suddenly, in 1970's James Bond fasion, the armed forces show up to save the day and mop up SPECTRE's ... I mean the remaning Thugee forces. It's a bit cliche (even for Indiana Jones) and seems a tad forced without the establishing scene. But, the Thugees are defeated, Mola Rom is well on his way through a reptile's disgestive track, Chatter Lal is a pancake, and the prince can get back to starting puberty.
13 ) Finale
This sequence is a bit too Hollywood, but there's nothing wrong with it per se. Indiana somehow gets to lead the kids back home to the village. (A few hundred of these kids want to know why they're in the wrong village now, but it's okay!) Indiana and Willie get their quasi-romantic moment, Short Round gets a laugh, and the Sankara stone is back at home. Cue credits.
As you see, this becomes a hard poll because the absolute worst part of the movie for me is the beginning of the much stronger second-half of the film. The first half really flounders a bit, with a couple of outright poor scenes, but nothing that makes you want to go see something less masochistic as the LSD trip. Some bad editing choices and 're-handling' of Willie in the first half really hurts the film overall.
Yes, the film is actually better than "Romancing the Stone", but it's pretty easy to see why casual $5 movie-goers would prefer the lighter-romp with Danny DiVito to a very uneven follow-up that gets downright masochistic at one point.