Hi Dznuts, I'm new and just a few weeks ahead of you with Mr. Beer and I experienced a similar situation. Mine was fully carbonated after 10-12 days but it still tasted like a sweet apple cider (green apple) taste, with a beer flavor behind it.
I waited another 5 days to crack open another and it was significantly better than the first but I'm still going to give it more time. Impatience has been my biggest enemy and although the 2 week beer is drinkable (almost), the 5-6 week Mr. Beer is something you'd want to share with friends.
If you're really interested in having a steady supply of your homebrew you can be patient with start looking on craigslist for a carboy/fermentor/more bottles so you can let them sit.
My best luck with Mr. Beer has been
-Keep it Clean!
- 2-3 weeks fermentor
- Use slightly less sugar than recommended for priming.
- 2 weeks Carbonating
- 3 days to 1 week in fridge
All these are minimums and another week at any step will not hurt. Also I've found if your sweet beer starts tasting sour you need to make sure your temperature is consistent and not to high!
Good Luck, and like I said if you have a patience issue like most of us beginners invest in another fermentor and in a few weeks you won't ever have to worry again. Also buy a hydrometer, it's 6 bucks and could save you six weeks of beer.