What technical details are preventing us from doing this instead of investigating more industrial ways which themselves will create other wastes?
You have to get more energy out than you put in.
To expand on this: Algae farming requires a lot of energy, therefore any large scale microalgae farming project may require too much energy to make it practical, and if the electricity supply is not clean then microalgae farming would actually be counterproductive to the goal of CO2 capture.
Current status and challenges on microalgae-based carbon capture
http://www.sciencedirect.com/science/article/pii/S1750583612001673
Full text: http://fulltext.study/download/1743320.pdf
...several recent life cycle assessment (LCA) studies have revealed that enormous energy input is required to cultivate microalgae and also for the harvesting and drying processes. The energy required (in the form of electricity) is normally generated from burning coal or natural gas that emits substantial amount of CO2 to the atmosphere and this could entirely eliminate all the positive effect of culturing microalgae for CO2 bio-fixation and biofuel production.