My sister and I did some moderate research into the idea of biodiesel and we discovered a lot of those problems. There are libraries of cultures that can be purchased from various sources around the world (university of texas was one of them I think). These are not specifically intended for biodiesel research, but rather generic stocks for general research so if you are able to get samples (usually runs close to $200 for each one) its entirely up to you to find a species that works.
Doubling rate, lipid concentration (by weight) and lipid extraction are the 3 primary obstacles in the idea.
Doubling rate is simply how fast it can grow. Generally high doubling rate strains are not very high lipid concentration. High lipid strains don't grow very fast. Bio engineering is one possible answer, but like Phantom already pointed out, this becomes a serious problem as a potential "bio hazard". Maybe thats a little harsh, but there are well documented examples of what can happen when the natural balance is thrown off by an introduced species.
Ultimately we figured the oil extraction process was the biggest problem. There are two basic ways to rupture the cell wall of the plant so the lipid can be released; chemical extraction which dissolved the cell membrane, and mechanical extraction which breaks it with brute force. This is where the total energy budget of the process starts to rear it's ugly head. More importantly, this has a direct result on the final efficiency in terms of how much energy you need to put into the bio reactor, to get a given amount of energy out in the form of a refined fuel thats ready to burn.
Chemical extraction (again, like phantom points out) is by far the most common way it's done and we discovered that even food grade cooking oils often used this method

. Chemicals used are basically refined out of crude oil so its not exactly an "eco" solution but they are reused and separated from the oil so in *theory* none of it needs to get in the final product (prove them wrong). Cyclohexane was the chemical we found to be used in many cases and was capable of stripping well into the high 90s for oil separation efficiency. Since this is a byproduct of refining crude oil I had to admit this was one way to make the process economical even though neither one of us liked it.
The lower the lipid content of the strain you are using, the more important this efficiency becomes.
Using a press was simple enough in concept but not very efficient and a lot of oil gets left behind in the "husk". Centrifuge was better but all this takes energy and I started to wonder just how cost effective this would be. Finding the equipment that could work for that also proved to be a challenge - no one seemed to have anything designed for this application. Ultrasonic was another idea that was even more experimental. OK, so what about using a solar plant to power the bio reactor? In essence this would now turn almost any diesel engine into a solar powered vehicle and possibly solve the energy budget issue. Things started getting complicated in a hurry.
Then there was the problem of feeding the algae since raw CO2 is not enough by itself to grow the stuff. The further we got into the idea, the more we realized just how hard it would be. Eventually we gave up. A year ago my sister had the chance to talk face to face with a biologist that had worked on the idea personally and without trying to discourage her, she basically said there is no easy answer (and likely had given up already). As it turns out even people with much more experience and resources at their disposal than we had, already came to the same conclusion. I guess that was some consolation for us.
Aeroscott does bring up an interesting point we discovered in our research. I agree that most of our crude oil reserves did NOT in fact come from generic dead plants and animals as is popularly assumed. Most of the oil came from plant matter and primarily from algae in it's various forms around the world including phytoplankton. This doesn't really solve the issue of biodiesel but it for me was the last straw in the idea of peak oil myth.
Simply put, any ocean floor can potentially be holding vast oil reserves for this reason. Why else would the russians want to claim the north pole as their own? Even though it's never been thoroughly explored, many know full well that there is likely to be a great deal of resources up there under the frigid waters. It's not exactly a comforting thought because even as a climate skeptic, I fully admit there are good reasons to diversify the energy economy of the world. And more to the point, de - centralize the global energy supply as well as the political power that comes with it.
I see nothing wrong with researching new ideas that could reduce oil dependency, but sometimes the desire to reach that goal has a way of clouding better judgement. I don't know if algae qualifies as a misguided effort yet but ideas like fuel cells certainly do in my view and yet vast amounts of research are still poured into an idea that has failed 30 years ago. Electric cars worked 100 years ago and they work even better today with more advances happening right now.
Biofuels from what would otherwise have been food crops are another good example of a failed idea under the pretence of being low carbon or green.
The MPGs are lower, the low carbon status (if that's your thing

) is dubious at best, the costs are higher, and worst of all this drove world food prices high enough to cause starvation the 3rd world to get significantly worse.
There is still a lot of potential though. Since Algae doesn't need prime farmland it can be cultivated in places that do not affect the supply of food. Also since its a nearly perfect balance of nutrition, it can be used as a high volume, low cost livestock feed to further free up farmland for direct food crops instead of indirect (ie, feeding cows). But as a biofuel, I don't see an answer anytime soon.