Would implementing more advances in farming save us from e-coli outbreaks?

That's a good question, and the answer likely depends on what advances one has in mind and whether or not the advances eliminate the causes and spread of E coli. Since E coli bacteria occur naturally within the intestines of animals and can contaminate just about any human food source unless it is killed before entering our mouths, it's almost impossible to eliminate entirely. Irradiation of all foods, which would kill all E coli, looked promising, but the exorbitant costs and concerns with long term health effects have hindered implementation of that tactic. In addition, having people adhere to the rigorous cleanliness practices necessary to avoid spreading E coli seems impossible as well. Hopefully an advance will come which will provide an inexpensive method for eradicating E coli before it enters human mouths.