I started getting this error many hours after I upgraded WP, and, matter of fact, I did not overwrite the wp-content folder at all, I left it totally alone during the entire upgrade process.
This error happened late and so I went and did just as you are writing about, chmod it to 777, I also went and read stuff and so I tried setting permissions back to 755, as it had been running all along that way previously. I never had done a 777 chmod and something I've read at DH states that 755 is what I need anyhow.
The point here is, I have chmod'd 777 and 755 both, and neither caused the plugin to work correctly since it started throwing the error. It's a sudden difference, and I have read about the allow_open thing other places, and looking into the inner workings of weathericon.php it does have two "fopen" statements, and that's what the error I was getting was about, I didn't copy it, and can't recall the exact language of the error, but it's the same one that I've seen other places regarding allow_open being disallowed on the server and "fopen" no longer working.
It is something that I don't care to delve deeper into. I ran this plugin just fine before, and now suddenly can't, despite multiple attempts to "fix" it. It's not anything important, so I just am moving on, and wanted to write out my saga to add to the thread. It might be that someone else can help, or it might help someone else.
It's simple probably to re-write that part of the code to do something else, but I have my mind occupied with bigger fish which I need to fry, and am not really a coder, just an HTML CSS coder with a bit of PHP savy understanding, not much though. :)