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Vienna airport boasts the minimum connection time as low as 25 minutes, "the fastest in Europe" as they claim. And Austrian Airlines frequently offers flights that are 25 minutes apart, including non-Schengen to Schengen flights. And sometimes it changes the schedule for already booked flights bringing them closer to 25 minutes.

In reality, when traveling from outside Schengen it is not possible to make this connection in less than 15 minutes, at which point the gate is closed. To get from non-Schengen area to Schengen area - even if you're the first at passport control and it only takes a minute - you need to walk quite a lot. I did this route three times, every time taking quite long walk which was no shorter than 15 minutes. And I was always the first at (empty) passport control and RAN all the way through - and I'm pretty sure that most passengers won't make it even in 25 minutes.

Every time I flew this route (OTP-VIE-SZG) I missed my connecting flight. Of course I collected compensation and got free overnight stay or a Mercedes taxi ride to Salzburg, but I'd rather be at my destination on time.

Is there a procedure where I, as a traveler, can challenge the airport's claimed "minimum connection time"?

The airline has made a deliberate choice to offer this connection by lowering the minimum connect time below what the airport recommends.

The standard time set by the airport is thirty minutes.

STANDARD.D/D...D/I...I/D...I/I.
ONLINE .30 .30 .30 .30
OFFLINE .30 .30 .30 .30

(D = domestic, I = international, ONLINE = connecting to the same airline, OFFLINE = connecting between two different carriers.) Before anyone asks, intra-Schengen counts as international for this purpose unless it is really a domestic flight in the same country.

The airline is allowed to create exceptions to the standard times. Filtering the exceptions table by OS-OS (Austrian to Austrian) and international-domestic, we get the following rules.

OS-OS ID .50 FLT 9772 - FLT 3527 
OS-OS ID .50 ALL - FLT 3501 
OS-OS ID .45 FLT 1 - 3499 - FLT 8721 - 8800 
OS-OS ID .45 FLT 1 - 3499 - FLT 8831 - 8920 
OS-OS ID .45 FLT 7071 - 7080 - FLT 1 - 9999 
OS-OS ID .45 FLT 8721 - 8800 - FLT 1 - 3499 
OS-OS ID .45 FLT 8831 - 8920 - FLT 1 - 3499 
OS-OS ID 1.00 ALL - FLT 3500 - 3999 
OS-OS ID .30 ALL - FLT 7001 - 7070 
OS-OS ID .30 ALL - FLT 7081 - 8100 
OS-OS ID .30 ALL - FLT 8121 - 9000 
OS-OS ID .30 FLT 7001 - 7070 - ALL 
OS-OS ID .30 FLT 7081 - 8100 - ALL 
OS-OS ID .45 FLT 8101 - 8120 - ALL 
OS-OS ID .30 FLT 8121 - 9000 - ALL 
OS-OS ID .25 

You can see that most services actually seem to fall through to the .25 (25 minute) rule, which is pretty surprising for a generic international-domestic rule.

Looking at the timetable it looks like OTP-VIE services are given a flight number in the OS 700-799 range; VIE-SZG services are given a number in the OS 900-999 range, so they are indeed caught by the 25 minute rule.

You can try complaining to Austrian, but I suspect they made a deliberate commercial decision to tolerate the risk. It presumably costs them money every day, so I would hope they already know about it.

Really, there isn't. It's the airline's responsibility to make things right if you miss the connection, so whatever they declare to be a legal connection time is up to them.

However, you, as a consumer, have the right to choose. I'd strongly suggest that you book flights with much more relaxed connection times - they should be readily available.

The only real risk would fall if your flights are rescheduled, in which case you could end up with a tight connection time again. If you do, I'd suggest calling the airline and requesting them to book you something with a relaxed time again, citing your original booking. I've had success with this in the opposite direction, where Air Canada rescheduled us from a reasonable connection to a very long one, and was willing to route us out of a different but nearby airport to get a more reasonable connection time, at my request, without any extra charges.