Nice question and interesting data! Going through the references of the linked site, one gets a more verbose description of the video:
After more than 1,000 nights of observations spread over 15 years, they have determined the spatial motions of more than 14,000 solar-like stars residing in the neighbourhood of the Sun.
For the first time, the changing dynamics of the Milky Way since its birth can now be studied in detail and with a stellar sample sufficiently large to allow a sound analysis. The astronomers find that our home galaxy has led a much more turbulent and chaotic life than previously assumed.
ESO Press Video eso0411 shows the stars studied during the present programme making their most recent orbital revolution around the Galactic centre before converging into the small volume where they were observed by the team. The duration of the video corresponds to about 250 million years. The yellow dot and white curve show how the Sun moved during this last of its about 20 laps around our Galaxy.
So this video shows the last orbit of the observed stars in the solar vicinity, starting at about one Galactic year ago, ending in the present state. In the press release they also link the paper by Nordström et al. with the scientific analysis which allowed them to create this backward propagation of peculiar motion of these stars.
In figure 30 they show the velocity distribution of the observed stars in the components U,V,W - a pretty uniform distribution, even when they can make out some distinct populations. So these stars with the "strange" orbits can be any or all of this: stars with very elliptic or high galactic latitude orbits (which thus only project to very elliptic in this face-on view of the disk. As to the reasons of these comparatively disturbed orbits they write in the summary, speaking about kinematic heating of the stellar orbits due to external influences:
Mühlbauer & Dehnen (2003) however, show
that when the true velocity dispersion and non-axisymmetric
disturbances of the disk are taken into account, large variations [in the velocities] can occur. The smaller exponents for the in-disk heating ($σ_U$ , $σ_V$ ) compared to the out-of-the-disk heating ($σ_W$ )
gives further constraints to be fulfilled by models trying to ex-
plain the observed kinematic heating of the disk. At least four
mechanisms have been proposed to explain the heating: fast perturbers from the halo, such as $10^6 M_\circ$ black holes; slow perturbers in the disk, such as giant molecular clouds; large scale perturbations of the disk caused by spiral arms (De Simone et al. 2004) or the bar (e.g. Fux 2001); and finally heating
caused by infalling satellite galaxies.
Mind also that these few stars which stick out with their orbits in this kind of plot or animation are very few compared to the overall number of investigated stars of 11k to 12k. They are over- emphasised as the dots of the normal - behaving stars overlap without transparency.