Here are a few things I've discovered. Some happened by chance; others came from fellow braiders.
When setting up a braid, just wrap the warp around the tama. Don’t bother tying it to the leader until you have to. (This works if the length of your thread is 36” or more). This lets you get to braiding quicker!
If you’re braiding with 40W rayon thread and finding the knots you use to attach the tama leaders don’t hold (rayon thread is VERY slippery), try tying an overhand knot in the thread close to the end and attaching the leader with a larkshead knot just above the knot in the thread. As long as you keep tension on the thread, the knot doesn’t come undone. The knot is easy to untie when there’s no tension on the thread, and the “kinks” totally relax when you steam the braid. I only do this with rayon; I use more traditional ways to attach tama leaders when I braid with other fiber.
If you’re moving 4 tama at the same time (2 tama in each hand) and having trouble placing them accurately on the mirror, try placing them one hand at a time. You still move and release them together, you just place them not quite at the same time. That way you can pay attention to one hand and then the other.
If your strands are getting tangled with their neighbors, keeping all tama at the same level will help prevent this from happening.
If you have trouble making all strands the same length when you let down your tama, use the one nearest you as the guide. Move the adjacent tama close to it and let them down so that they hang at the same level. Then use them as the guides for the next ones, and so on around.