So I just brewed my 2nd batch ever yesterday and since it was a nice day, I decided to brew outside. As I was cleaning everything up at the end of the day, I realized that I forgot to put a cover on the pot while it was cooling after the boil. Since the beer was sitting outside with no cover for bout 45 minutes after the boil was over, what are the chances that this batch is ruined?
Short answer—you're fine. Long answer—you're probably fine. 45min isn't that much time for nasties to get in (unless, say, a leaf fell into the kettle) and if you pitch viable yeast they'll likely overpower anything that did make it in. That being said, give the airlock a sniff every few days. Your nose will know if something is amiss...
I'm not sure why you would cool with the lid on. It would take much longer to cool your wort that way.
Never cooled with a lid and I always brew in the open. I think I'd bet on quicker to 75 degrees over random stuff getting in for higher chance of not getting nasties. Unless there was a lot of stuff blowing around, then I'd probably improvise some kind of porous cover.
You should be fine. But definitely work on getting down to 70's quicker. What method are you using to cool?