I don't mind instructors in a frayed or "distressed" gi--belt, either. Like GD said, it indicates that the uniform has been used and used well. I have gis that are so worn out they are no longer black, but grey.....and I will wear them from time to time for class.
If a uniform is torn to shreds, or torn to the point of being indecent, or is otherwise not wearable, then yes, my opinion is that it should be retired. Likewise, I feel that if an instructor is doing a public demonstration, or lecturing in uniform, or anything similar, then it *might* be best to wear a newer, cleaner, and less "worn" uniform to present a good image. Again, like anything else, this will depend on the instructor, on the audience, and about a million other things.
Belts, well, there's another debate that has been hashed over endlessly on these forums. I respect a frayed BB, if it is legitimately frayed, and not something that some goof took sandpaper to. If it is frayed due to use, then it is worthy of respect, in my opinion.
When I am at work, I dress in business casual. When at home, I tend to prefer sweats or jeans. When instructing at our school, I wear a clean and pressed uniform (red top, black bottoms). When in class (black uniform), I wear a clean and pressed uniform. However, I may just be wearing the "grey" one.....it's like the pair of jeans that finally fits "just right".....that'd be my "comfy, gettin' down and dirty" gi....
Peace--