The second thing has to do with the depth of field. Stabilization effects can often fall apart and get the jitters (that jello look) under these conditions.
Stabilization software is great but can be incredibly demanding under low-light conditions. The first is to always make sure you record in a well-lit environment. Both of them have to do with how you shoot your video.
When you’re shooting your videos, there are two things to keep in mind if you know you’re going to be stabilizing the video in post-production. Tips for stabilizing video in Premiere Pro