I've never had the problem with continuity that so many others seem to have. Whenever the discussion of Marvel/DC books comes up, continuity is almost always the go to negative that is given.
When I was young, I tended to just get whatever comic caught my eye. Sure, there were characters I liked that I would actively look for, but I'd pick up books at random just cause I liked the artwork or something.
There were always things going on that I didn't have the background on, but I don't remember it ever bothering me. If I liked the book I'd just file it away as "stuff-that-happened-before" and pick up the salient points through recaps or other sources (Wizard magazine, etc.)
Of course, once the internet began coming into it's own, finding out any plot points I was curious about became a non-issue. But even before that, the continuity never turned me off or frustrated me.
Then again, I've found as I've grown that I appear to be notoriously easy to amuse. So maybe I'm just being too easy on the whole thing.