What immediately bugs you when watching an episode? Mine is when they transport someone sitting down and they reintegrate in a standing position (or vice versa). Sure, the tech is near magical but my suspension of disbelief pretty much snaps when they do this.
One thing on TNG that always bugs me is when they know something is wrong or they lose contact with Starfleet personnel, and the Enterprise goes to warp 7 instead of maximum warp! It’s not until there’s an extreme emergency that they go to maximum, and often they could have avoided that emergency by showing up a half hour earlier. I know they came up with the whole warp speed limit thing, but it’s still something I notice.
Something that’s not an in-universe thing but still bugs me is the writer’s lack of acknowledgement of three dimensional space and orbital mechanics. It’s an issue with much of science fiction though.