Oxygen accident.. Beer ruined?

Ok, so I just used whole hops for the first time. While siphoning my beer into the keg (I have the pump style siphon), hops got stuck in the siphon and someone sent a lot of bubble into the beer. I cleaned the siphon out, sanitized it, and started again more carefully, but it happened again. I have two questions:
Will the oxygen ruin my beer, and if so, how long might I have before it starts tasting bad? I realize this probably depends on the amount of oxygen, but any input is helpful.
How can I avoid this problem with whole hops in the future?

Thanks guys!!!

I should add that these were from dry hopping.
If anyone is interested, it's an all-Amarillo IPA, and right now it tastes awesome!

It takes a lot of oxygen to ruin your beer, usually a lot more than basic mistakes like that. I've done the same thing, and my beer's turned out fine. Effects like that are long term storage issues anyway, so usually you would have finished drinking your beer long before any of that took effect. Relax. We've all done worse to out beer and it's managed to survive.