Is the Tomasi-Kanade factorization still commonly used as a modern computer vision technique?
The Tomasi-Kanade algorithm is probably not used too much these days, though it is an important algorithm that provides a lot of insights and opens interesting avenues of research.  I would say that the main drawback of the algorithm is not that it assumes an orthographic camera, but that it requires a full data-matrix, in which all points are visible in every view.  This is usually not realistic in practice.
The most significant step to address the first issue was the Sturm-Triggs extension of the algorithm to true perspective camerad (i.e. the pinhole camera model).  There were several follow-ups to this, trying to improve on the original method, including papers by Shyjan Mahmood, John Oliensis and others, to a point where the algorithm works well for the perspective model, as long as points are visible in all views.
The situation where there are gaps in the data is addressed by the research topic of low-rank matrix factorization with missing or noisy data.  Unlike the low-rank factorization of a full data matrix, where a least-squares solution is available using SVD (as in the original Tomasi-Kanade algorithm) low-rank factorization of a matrix with holes, or per-entry weights, is NP hard.  Nevertheless, various methods of trying to do this have been proposed, and a good place to look at this is the paper &quot;Damped Newton Factorization for matrix factorization ...&quot; by Buchanan and Fitzgibbon.  This discusses and compares various methods.
Essentially the same sort of algorithm is used for dynamic structure and motion, or multi-object structure and motion.  A good place to start looking into that is the work of Rene Vidal, who has looked at these problems in great depth.