I don't tend to notice small errors like "oh the artist forgot to draw the patch on the arm of his jacket!" if I'm absorbed in the story. Sometimes Andrew Hussie forgot to draw the horns on Aradia in Homestuck and I didn't even notice!
What I do notice though... When the artist doesn't seem to know what their character looks like apart from their clothes and accessories. When just the general body proportions, posture and faces of characters change drastically from panel to panel because every panel is referenced from a different comic or illo, or they're using stock photos for reference that aren't all of the same person or even particularly similar looking people. I can really tell when somebody's mental image of their character isn't, "I imagine she has a heart-shaped, elfin face, you know, like Audrey Hepburn, with a very defined little nose and a high browline." but "IDK, I imagine she looks hot. Like just any hot lady." Sure, most artists settle into how they draw a character over time, but when there's no consistency within the same page (and it's not a clearly deliberate style shift for comic or dramatic effect) it's like... this feels weird, as if the character keeps changing to a new actor in the same costume every time there's a new camera shot of them.