Number one is the continued references to Keplers laws. Kepler only applies to 2-body systems where the mass of one is dramatically larger than the other. This works well for the solar system, where the sun is huge compared to the planets and the planets have little effect on each other. But do note that some planets were predicted to exist based on their effect on the orbits of other planets, so even in this sparse system the effects do make a difference. My point is that Kepler has no place in galactic dynamics but is often referenced - if that were the model that doesn't match observation then DUH! But the physicists are smarter than that.
Second, I occasionally see mis-application of the divergence theorem and/or gauss's law. Some folks seem to treat a portion of a galaxy out to a radius R as a point mass by using this theorem. The problem of course is that to make that leap you must have a uniform spherical distribution of matter inside the spherical boundary. In other words, a disk-like distribution of matter does not have a uniform gravitational pull at all points of distance R from its center. You'll find it is stronger near the edge of the disk than at the same distance perpendicular to it.
Third, this particular article keeps making reference to the "radial velocity" or speed of stars where I believe they are actually talking about the orbital or tangential velocity.
And lastly, if the dark matter obeys the same laws of gravitation, there must be a reason for its distribution to be different than the other matter. At that point, I don't see any need for "strange dark matter" or new particles or physics. You really can't have it both ways - it's fundamentally different, yet it obeys the same rules. Having said that, I could see how exploding stars would spread non-visible matter (remnant material) in a way that might be very different from the stars themselves.