I set my sewing machine on a microfiber cloth. All the thread attach there. (there is no cleaning that cloth, I just rotate it, and flip it, until it is totally covered with threads, and then get a new one.)

I really don't have a problem, but I do so much chain sewing that I don't have many threads. The only thing the washer and dryer can't handle is a microfiber dishcloth. I wonder if one would be better for thread removal than a lint roller. When I was using lint rollers on my pants when I was working, the dog hair clogged them so quickly. There are some loose threads on my design wall. I will try a microfiber cloth and let you know.

This brush will take thread and pet hair off anything. I was skeptical but it works.
http://shop.flylady.net/p/(RUB-BOGO) Now it's buy one get one free.

Mine gets mixed in with the dog hair on my shirt! Seriously, using Guterman's polyester avoids the problem for me. I also have a "cat food" can beside my machine and pick up threads as I sew.

When people ask me what my clothing style is, I answer "dog hair and thread". LOL

I wear jeans & knit shirts when I sew. The threads don't stick to them too bad. I like the idea of making an apron of a tablecloth so that the threads shed off. That would be cute with some type of binding around it and wouldn't be hard to make. I wear an all cotton apron when I cook with good clothes on. I don't know why that wouldn't work for sewing.

I made and wear Janet Clare’s Artisan apron, there are lots of patterns on Pinterest for similar styles and it keeps my clothes clear of thread most of the time ;)

About stray pieces of thread: I just tell people, "I come with strings attached."

We purchased an under-desk mat for under the table where I quilt. It's a hard surface, flat, so easy to clean up.

I use a bristle brush, also known as toilet cleaning brush - that has never seen a toilet - to "scratch up" threads from the rug. It works.

I wear demon jeans & shirt for some reason threads do not stick to these. If I wear a sweater it's a thread magnet.

Cat hair and thread is a fashion accessory in my house.