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.
Base Breaker: Bond dressing up as a clown during the first climax. Depending on who you ask it's either too silly (even for a Bond film from the Roger Moore era) or it's an acceptable, some daresay even clever, way of showing just how desperate Bond is as he races to avert tragedy.
Hilarious in Hindsight: The first climax involves Bond successfully deactivating a nuclear bomb - something he couldn't do almost 20 years earlier in the climax of Goldfinger.
Kabir Bedi, who plays the evil henchman Gobinda, also appeared in the low budget horror film Satan's Mistress around this same time with former Bond girl Lana Wood (Plenty O'Toole from Diamonds Are Forever).
Les Yay: There are a couple of looks exchanged between Octopussy and Magda that hint at sexual tension. When Magda protests letting Bond go through with his antics at the circus she sounds like an annoyed girlfriend, and the look on Octopussy's face in response to this practically screams Can we please not do this right now?
During Kamal Khan's literal manhunt, Bond swings through the trees, complete with Tarzan yell.
Narm Charm: The infamous scene where Bond is dressed as a clown is actually quite tense and suspenseful, what with nobody taking him seriously while he's desperately trying to warn the generals of the nuclear bomb that's about to go off. "Let me go, damnit! There's a bomb in there!" What really seals the deal is that we actually see the bomb's counter hit 0, as Bond disarms it at literally the last split-second.
They Wasted a Perfectly Good Character: Octopussy was built up to be quite a formidable woman with her own empire, but the few times she engages in the action she gets beaten rather easily. Kind of a shame considering that actress Maud Adams actually did have good chemistry with Roger Moore.
Unfortunate Implications: Bond in India is never going to end well. Octopussy still does a lot better than Indiana Jones and the Temple of Doom, but it's still uncomfortably neo-colonialist, especially Bond's remark, after tipping an Indian driver, "that'll keep him in curry for a while!" It's treatment of women - never a Bond series strong point - is poor, and the not-so-subtle implication of Stephen Berkoff's mad Soviet general is that nuclear disarmament and peacenikery are doomed to failure because Reds are evil. See here.
That last point is extremely debatable, given that every other General on the council besides Orlov wants peace with the West and thinks that Orlov is nuts.