When you use a "stop bead" to keep the beads from sliding off the end, choose a bead that is a different color or size. That way you won't accidentally incorporate it into the piece on which you are working (and ruin the pattern).
If you have trouble threading the needle, try flipping the needle over and coming from the other side. Needle "eyes" are stamped out and so one side is a little wider (making it easier to get the thread through) while the other may have burrs that hinder threading.
When you are bead stringing, use a clothes pin or an "alligator" style paper clip clamped on the end of the wire to prevent the beads from sliding off. It works better than taping the end, and doesn't leave any sticky residue.
To help keep the tension of your weaving even, try holding the piece in your non-dominant hand (in my case the left hand). After you tighten the thread, fold it over your pointer finger and clamp the next finger on top of the thread. Because the thread is caught between your two fingers it can't loosen up. Pick up the next bead, but don't turn loose of the thread until you are ready to tighten the new stitch.
If you are using Square Stitch you can take any cross stitch pattern and do it in beads. This opens up a whole new world of patterns and works every time. With a little bit of adjustment it will work with Peyote and Brick Stitch, too.
When using toggles as closures, remember that the bar side of the toggle must have enough distance from the bar to the beads in order to pass through the ring of the toggle. If the last bead on the strand is too big to go through the ring, and the bar is attached right next to this big bead, you won't be able to get the bar through the toggle ring (I learned this the hard way!).