In any case, I'll be bringing a new, arguably more reliable, person into the mix. One (very famous) Tom Caster, who also recently found himself with an abnormal amount of free time and an interest in brewing.
Tom recently ruined a batch of extract Hefewizen. Well, ruined isn't quite the right word. He cracked a bottle the other day to discover that his hef was as flat as the world in 800 AD, and that it tasted sweet and only slightly beer-like. No other off-flavours were noticeable. I discussed with him a few of the possible causes of such a horrible malady:
The first problem could have been that primary fermentation never finished. In this case, the sweetness is caused by the residual sugars that the yeast never really got around to eating. The lack of bottle-conditioned carbonation is a result of the fact that, well, there aren't any yeast there to do their jobs. Primary fermentation can fail for a number of reasons. It's summer, and it's hot. Heat can slow down yeast, cause them to produce undesirable flavors, or in the worst cases, outright kill them. Additionally, some types of yeast flocculate out extremely well, and after only a few days of fermentation, all the yeast in the liquid might have settled to the bottom. This is easily fixed by agitating the fermentation vessel in order to stir up the yeast, but if one does not know to do this, the yeast will just sit at the bottom, not finishing their wonderful Krausen cycle.
The second cause could have been that there weren't enough yeast left in the liquid to carbonate the beer. In this case, the sweetness would be caused by the sugar that is added to the fermented wort. Because this sugar is never eaten by the yeast, you'll taste it in the final beer.
Lack of yeast in the bottled product can result from the over-flocculation described above. It can also happen because of excessive filtration, especially when brewing a heavy beer that you might want to ferment in three separate vessels over the course of several weeks. By the time you're bottling, the concentration of live yeast in the liquid simply isn't high enough to do anything with the sugar that you've given it.
This is all, obviously, assuming that primary fermentation proceeded far enough to generate some alcohol. If no alcohol was generated at all, well then you've just left a bacterial paradise sitting around for three weeks. I wouldn't drink that if I were you.
Tom didn't take the original gravity of his brew, so we don't know the final alcohol content. Tom determined that his brew was safe through the time-honored practice of taste testing. No off flavors? Not going to kill you (probably...).
So Tom will be repitching the entire batch. Opening all those bottles, pouring them into a carboy, repitching the yeast, agitating once a day for two weeks, etc., etc. What a pain in the ass.