Disclaimer: I am not an anti-vaccination nutjob. The following post refers to the flu vaccination, and the flu vaccination only.
First off, with regard to TFA, this alone should not discourage people from getting the flu shot. The simple fact is that the "swine flu" is the same as the "regular flu" that we get every year. It is not particularly more infectious or deadly in any segment of the population than any other flu strain. The fear surrounding this particular strain is simply manufactured by the media. If the flu vaccine reduces the chance of getting the other 15-20 strains of flu by a significant amount, but doubles your risk of this particular strain, you still come out ahead.
However, most people should not even consider getting a flu shot in the first place. If you are between the ages of ~15 and ~60, and are in general good health, you should not get the flu shot. It terrifies me when I see flu shots being given out to students at local schools and colleges. These are the people who have absolutely zero risk of dying from the flu. None. Even if it leads to pneumonia, there is only a risk of death if proper medical treatment is not given. The worst that can happen is, well, that they catch the flu for a week or so.
The flu shot, on the other hand, can be extremely dangerous. My aunt was a nurse, and thus was required by her job to take the flu shot every year. She had been taking them for nearly a decade when, in her mid-thirties, she was paralyzed from the waist down by the side-effects of the flu shot. Had she not taken the shot, the worst that would have happened to her would have been simply getting the flu. She got a large settlement from the vaccine manufacturer and her employer. It was a rather fast process, as they knew beforehand that a certain percentage of people who take the flu shot would have this reaction. The cost of the settlements is simply rolled in to the cost of the vaccine. A couple of years later, a friend of the family suffered similar complications from the flu shot, and died. He was only 28 at the time, and in perfect health. Had he not taken the shot, the worst that would have happened to him would have been simply getting the flu.
The results of this study are interesting, but they make little difference. The vast majority of people should not be getting the flu shot in the first place. Taking it is simply rolling the dice unnecessarily. For those who are very young or old, the risks from the flu shot and the risks from the flu itself start to even out. In that case, the shot may indeed be a better idea. The results of this study do not change that fact.