Money. Unfortunately VCs and Angels in Boston have a very poor reputation for taking risk on startups. Instead they want to invest in companies that have already proven their model or just need money to scale.
Public transportation. I know that every city dweller thinks their city has poor public transportation options. Let me tell you, Boston has you beat. When we take into consideration the perceived importance of the city and how difficult it is to get from one side to another.
Insider's club. Unfortunately Boston still has a pretty strong insider's club that affects most aspects of business in town.
Racism. Boston has a bad history of racism. For a city that prides itself on being so progressive this is a black eye that I personally don't feel the city has gotten over.
Weather. I know that this point was dismissed in another comment but it just isn't about the winter. The two months of cold grey sky rain in the early Spring is curshingly depressing.
Lack of a true "anchor" tech company. There really is no large tech company that draws others in or produces talent. Many here think that Hubspot will be that company, that remains to be seen.
San Francisco envy. It is pretty pervasive here. We call it the Boston Brain Drain. The perception is that Boston is just a stepping stone on a developer's career. "I learn in Boston I work in SF!"
Cost of living. I realize that SF and NY are more expensive but Boston I suspect that you get more for your money in those cities. In Boston $3k/month will get you into a triplex in Somerville with no T access. Living in Boston is out of the question for many making below six figures. (also for many making above six figures)
Cost to run a business. I can count on my hand the number of neighborhoods in the city that have office space below $30/sq-ft. Nearly everything in the city is North of $40/sq-ft. And for that you get some run down Class B office space that was recently bought by a Class A property company that wants high-end Class B rates. And they are all pushing $1/sq-ft increase per year. With nearly $2/sq-ft utilities. Startups looking for private office space have a difficult time finding any in Boston.
All this to say that the medical industry does not have this same talent retention problem. What keeps the world's best doctors in Boston but pushes away the world's best software engineers? If Boston wants to make up ground on SF (and even NY at this point) I think starting with this question might lead to potential solutions.