Of course there are legal problems, but there are for scans too, it won't be any different. It wasn't that long ago that famous scans website, BW Greyscale, was forced to remove the majority of their fashion magazine scans by the publishers because they were threatening to sue. All magazine images are copyrighted, which usually means you're not allowed to reproduce them -> scanning is a way of reproducing them, so technically, it's not allowed. However, most magazines and publishing houses don't pursue this aggressively, you're not likely to get in trouble. Whether or not this changes with digital versions, only time will tell!
However, when I ripped HQ videos from the iPad app for LOVE Magazine a little while ago, and put them on YouTube, the official LOVE magazine Twitter retweeted my video, so they didn't seem to mind. Your mileage may vary!