As you are always stitching onto the top layer of fabric, points can lose their definition rather quickly and ruin the look of your work. Try this out as the drawings.

Stitch one blanket stitch on the point and then carefully do one more straight stitch stopping with the needle down. Turn the work with the needle down, then manually lift out needle raise your pressure foot and pull the work slightly away from you, then complete the horizontal blanket stitch.
This means you are away from the corner and will not get a great lump of stitches where there is to be a point! The two straight stitches, one before and one after the corner make the point show up sharply and your quilting friends will be very impressed!

Now when stitching a 90 deg corner, try this. Stitch right to the corner completing the horizontal stitch of the blanket-stitch and one straight stitch, then with needle down swivel the work and do one complete blanket-stitch in the corner, turn with the needle down and continue on.