Question: It has become clear that I need to practice my transfer techniques; I just completed a primary-to-secondary transfer which involved what I'm guessing is a fairly significant amount of aeration. During my transfer (1-gallon basic brown beer, direct from carboy to carboy; no intermediate pot), I used an auto-siphon, and ended up pumping oxygen in. In addition, there was air in the line even while the beer was flowing (which I had to restart several times).

Ultimately, if a beer gets aerated, is it a solid bet that the beer will be oxidized and pick up that "musty, cardboard, stale odor and flavor"? Should I not get my hopes up, or might things still work out?

**Update:**

Last night, I opened one of the bottles. Much to my surprise, it was *not* awful! The carbonation was a little low, it could have had more flavor, and it was a *little* stale, but it was not the disaster that I was expecting. Hooray!

Answer: 
I'd say keep your hopes up. Unless you pumped a ton of air through it, I don't think it will absorb as much as you think it will. The real problem comes when you slosh it around in the carboy afterwards if you are moving it to a fermentation vessel or closet somewhere, since you removed the layer of CO2 that was resting on top of the carboy and replaced it with oxygen. If this is a concern, transfer it where the secondary carboy will be sitting for secondary fermentation, and don't move it, or use a CO2 tank from a kegging system to purge out the oxygen with CO2 before capping it with an airlock and moving it around.

Try a few basic things to keep from oxidyzing during transfer:

1. Keep the "out" end of the rubber hose submerged in the beer in the secondary carboy until the very end of the transfer has completed. Also, keep it at the bottom of the carboy, so it isn't splashing when beer goes in.
2. Keep the "in" end of the siphon always submerged in your primary vessel.
3. With your auto siphon, don't ever use it to transfer hot (as in a boiling or near-boiling) liquid, as it will deform the auto siphon and may ruin the seals necessary to keep air out when transferring (personal experience on this one, my first half-assed attempt at fly-sparging).
4. Depending on the platforms you are transferring to and from (where your two carboys are at when siphoning), make sure you have more than enough tubing for your siphon. Don't cut yourself short and have to complicate your siphoning process by stacking books under carboys or moving chairs around, just keep it simple and get the right amount plus a foot or two extra, it'll save you a huge amount of hassle.

With experience you'll get better, you just need to try it a few times to get it right. The important ones are steps 1 and 2 above. As long as you keep both ends of the siphon submerged during transfer (past the beginning couple of seconds), there's no way for air to mysteriously get in until the very end, at which point you simply pull either end out and the suction will not pull further air into the wort.
Why would you need to restart the siphon several times? With an auto-siphon, you should have one or two strokes of the wand, and then it siphons until finished.

Also, why are you doing a transfer to secondary at all?

As for air in the line during the transfer, I find if I pinch, rotate and/or constrict the flow near that point where a bubble is present, you can usually "fill it in", and get the bubble to clear.