I just found and booked a flight from Japan to Australia.
I found the flight with SkyScanner.
That site redirected me to the online travel agent airtickets.com.
The flight itself is on JetStar.
Now the odd thing was that at the very end of the booking, after entering my credit card details and some stuff my bank (ANZ) asked me to complete along with it, I ened up getting an error on screen saying this or almost almost exactly this:
An error occurred. Please try again later.
Yet I received three emails from airtickets.com saying the transaction went through. There are numbers: a "reservation number" from the travel agency, and a "ticket number" from the airline.
It also seems that the appropriate amount of money has become unavailable to my credit card according to my online banking, though the specific transaction has not shown up there yet.
When I try to verify my flight via the airline it asks for my number and email address, but then tells me if I booked via a third party that I can only check via the third party.
When I try to verify my flight via airtickets.com their website only takes me to a page where I must choose between cancelling and changing my ticket once I enter my number and email address.
Since I don't believe there is no possibility of cracks in the system, how can I verify that my flight is truly booked and not going to be reverted by some automation in the system that detected an error occurred?
I'm now more confident, but still less than 100%, by doing this:
I could log in at https://checkin.jetstar.com - this address is designed for doing an advance web checkin, rather than for confirming your flight.
The JetStar system does currently contain my name and flight details but it's too early to do the web checkin itself. I get this message:
Your flight from Tokyo (Narita) to Gold Coast is not ready to be checked in yet. Please come back 48 hours or less prior to your flights departure time.
It's annoying the JetStar lets me log in here but not in the place for checking bookings. Having had unexpected things happen due to the strange logic of such systems before, I'm still not 100% convinced it's permanent and can't be reverted by error checking systems.
A friend in the airline industry got another friend in the airline industry who has access to the appropriate tools to look into this for me. The result is that my six-digit alphanumeric "ticket number" is indeed a confirmation that I have an e-ticket booked with JetStar.
Just now I checked my online banking and saw that the transaction has now gone through fully.
There will be one more update from me after I've been on the flight. Or with some shocking news if that turns out not to be possible...
(Not posting an answer because I don't think this could be re-usable by another person in a similar situation.)