As far as off flavors from O2 in secondary, you probably should be fine. I've gotten into the probably unnecissary habit of purging O2 from my secondary the same way I do my kegs with my CO2 tank from my kegging system, but that's just b/c I'm paraoid.
When you transfer to your secondary, some of the CO2 created by the primary fermentation should come out of solution and since it is heavier than air it will for a protective blanket which should keep off flavors at bay. Off flavors from O2 typically are of the wet cardboard variety, it will be fairly noticable if present.
Also it's probably not your brewing skills getting worse, but your tasting skills getting better. This will cause a very positive effect on your brewing skills, as you can find and fix problems you didn't know to look for in the past.