We spent the day discussing Milky-Way halo and disk structures with Amina Helmi (Kapteyn). It was fun! Along the way, Adrian Price-Whelan (Princeton) and I spent time looking at large halo structures that have been found in the literature. We could find some extremely odd structures when we match the cuts used in the papers we were looking at. And then we found the following:
Say you are cutting at parallax signal-to-noise of 5 (parallax over parallax error greater than 5). And then you look at the configuration-space shape of the stellar distribution you find? Well guess what? Since parallax errors are a strong function of sky position, the shape of your object will be very strange at large distance. For instance, the parallax errors only go below 0.05 mas in some parts of the sky. So your stellar distribution will only extend out past 4 kpc in some specific directions (and not all directions).
All this relates to various things I have said repeatedly in this forum: Build your science on measured quantities, not estimated uncertainties on those quantities! Your uncertainties are not really your data, and it is almost impossible to know your uncertainties on your uncertainties. Furthermore, the people who want to cut on parallax signal-to-noise are also using inverse-parallax as distance, and that's dangerous too. Finally, if you cut on parallax signal-to-noise, you will bias any means or averages or regressions you do using those parallaxes.
My advice: Find ways to work that don't require these cuts. These issues are a big danger for people using actions to study the stellar distribution: Actions require distances, distances are generally inverse-parallax, and then low signal-to-noise parallaxes must get cut. These arguments apply there too. We have to forward-model the data if we want to understand spatial structures, I am afraid.