Jury nullification has to do with returning a "Not Guilty" verdict in the face of evidence that would suggest otherwise.
What you are talking about it a "hung jury" where the 5% person is able to prevent a unanimous "Guilty" verdict. Depending on the state, the requirement for conviction may be unanimity or something less (11 to 1, 10 to 2, I don't remember if it goes any less). In this cases, the prosecutors may choose to retry the defendant - if you think about it, if the prosecutors decided to try him once, why not twice? The odds are the same the second time around (i.e. the odds of not getting the 5% person on the jury).
Regarding "bogus convictions", the jury only gets to make its decision when a high enough evidentiary threshold is met. Otherwise, the judge must throw the case out for not meeting minimum requirements.
Think of it like this (note that this is my own approximate guesses taken from my law school class on Criminal Law) - "Reasonable doubt" may be a 95% confidence threshold for the jury to convict. For the decision to get to the jury, the judge has to decide that the evidence is at least 75% confidence level in his opinion. Its only 75% for the judge because he is not the finder of fact and the jury can reasonably decide that what the judge views as 75% certainty of guilt is actually 95% in their view.
So to sum up, the situation is not as dire as you would suggest. I agree that jury nullification can be a big problem in the wrong situations (racist communities, etc) and that is why the law tries to minimize its impact (e.g. defense attorneys cannot mention jury nullification to a jury during the trial) while preserving defendants' rights to a jury of peers.
Like seemingly every aspect of law, there isn't a clear cut answer either way.