If I understand the chronology correctly Prudie, Aspartame was originally approved for use in dry foods back in 1974. There was quite a high profile campaign and legal action challenging that approval, so the FDA approval was put on hold in 1975. At that point, Searle had not sold any Aspartame.
The legal argument and various internal reviews, challenges, correspondence and collecting additional safety evidence through further studies a public inquiry in 1980 etc took around 6 years, so Searle were not able to sell Aspartame until 1981.
http://www.gao.gov/assets/150/145477.pdf
Since then, there have been many more safety studies. Many more trials, and several comprehensive reviews of the evidence, all of which have found Aspartame to be perfectly safe.There have even been european conferences on aspartame, discussing its safety etc.
http://www.sciencedirect.com/science/article/pii/S0278691507000798
The most recent review was conducted by the EFSA, originally scheduled to report in 2020 I think, their report was brought forward for release in 2013. They have been able to review over 30 years worth of data, studies, reports, public enquiries, and concluded the Aspartame was safe.
With this level of scrutiny, with this many studies and reports,there are few food additives out there that could be considered safer :)
http://www.efsa.europa.eu/en/topics/topic/aspartame.htm