Mahler himself specifies long pauses between the movements of various symphonies (most famously at the end of the first movement of the 2nd; I think somewhere in the 5th too but I forget where).

Surely applause is entirely natural at the end of the first movement of the 3rd? Everyone's been concentrating like mad for half an hour or more and the movement's ended with a great big crash. Seems only fair to relax for a bit. Not like clapping at the end of the fourth movement, for example, which would be a bit silly.

It just occurred to me that some of his symphonies are divided not just into movements but into Abt(h)eilungen, each of which may comprise several movements or just one. The first movement of the 3rd is its own Abteilung, isn't it?

There are more than a few works in which the internal drama and sense of momentum is generated in part by the sense of the individual parts as some continuum. For my tastes, clapping between these can render this overly diffuse and lose some of the focus and tightness. One example would be from Die schöne Müllerin, specifically between 'Eifersucht und Stolz' and 'Die liebe Farbe'. If there is applause after the relatively virtuosic piano ending of the first, the sense of a void opening up into which the pained tones of the successive song appear is considerably lost to me. Even worse is to applaud after 'Mein' (and to be honest it's not a song I particularly care to hear out of context, as that changes its meaning so much), so the sudden shift of gear in 'Pause', unexpectedly in the flattened submediant of the previous song (for which the two preceding songs can retrospectively be heard as a dominant), drastically defamiliarising the young miller's sense of euphoria (misplaced, as we certainly discover soon afterwards, and arguably have sensed previously). Clapping between movements in a work like this, even if it was common in Schubert's time and soon afterwards (but common practice does not equal compositional preference - also, Schubert never heard the cycle complete, that had to wait until several decades after his death, in the voice and hands of Julius Stockhausen and Brahms), exacerbates the sense of its being just a collection of numbers sung in a particular sequence, rather than the much more integrated work I believe it to be. In some operas the situation is very different, of course, especially those many in which the plot and drama essentially acts as a thread on which to hang ear-catching 'numbers', but still this surely needs to be judged on a case-by-case basis.

The physical circumstances of 99% of opera performances really dictate this anyhow...  while a podium-placed concert soloist, or concert-hall conductor can gesture to the audience that applause isn't wanted at this moment,  an on-stage character can't motion to the "fourth wall" to shut up (without breaking the essential "suspension of disbelief" rule), and the conductor is usually buried too deep in the pit to be able to do so without bending over the back wall to the audience. There's certainly a genre of opera which expects (and encourages) audience applause after "warhorse" numbers - the "rattle-rattle" codas in Rossini's set-piece arias seem especially intended to act as a prompt to do so. However, I think many attendees at operas will take their lead on this from whatever they can see of the conductor's baton...  and if it's clear he intends to take an attaca into the next number, will hold off from applauding.

However, not all opera houses have such ideal pit arrangements.  At Helikon-Opera in Moscow I've seen the conductor step off the podium (which is located between seats A-15 and A-16) into Row B, and say "Can't you for chrissake shut up?!" in a hissed whisper to a talkative member of the audience at a performance of LULU.

There are quite a few "they think it's all over" moments where applause might come at the wrong moment in opera...  early bel-canto operas which have solo numbers in the "aria+cabaletta" format (such as "Vien diletto, è in ciel la luna" in PURITANI) shouldn't have applause between the sections, because the soloist "isn't done yet".  Verdi harnessed the convention to create the "scena", a soliloquy in which doubt or confusion audibly gel into conviction and/or determination...   but unfortunately often audience enthusiasm tramples over the idea, and "E strano.." is chopped-away by applause from "Sempre libera.." in the same way Ian mentions in the Schubert above, impacting poorly on the dramatic result.  Even worse, the modern generation of diva actually stops to acknowledge the mid-way applause

Probably the toughest scena to keep going without intermittent applause is Tatiana's Letter Scene from ONEGIN, whose disparate sections should really continue to the very end before the audience acknowledges their appreciation.  Once again, however, this rarely happens.

Most amusing case of inappropriate operatic applause for some while: there is a youngish tenor in Moscow called Nikolai Baskov, whose former career as an estrada star ensures that the paparazzi follow his every move.  Baskov was - after much trenchant refusal - finally given a performance at the Bolshoi, as Lensky.  His claque were duly paid to sit amongst the audience and cheer him at every turn.  As Scene Two opened, the Estate Workers sang their little wassail song from offstage to Mme Larina, opening as it does with an unaccompanied tenor solo.  "Bravo, Kolya! Bravo! Superbo!" was heard blasting-over the pianissimo chorus passage that follows.  Of course, Lensky doesn't sing a note for at least another five minutes...    After Lensky's death, at least 80% of the audience left the theatre, causing havoc in the cloakrooms who weren't ready for this exodus...  they apparently didn't realise (or care) there was still another Act to go..

Yes, I'm afraid so....