As always Nicole, great article. As you note, multiple choice tends to be the "default" for many designers, and they're not bad, but designers should consider other options too as you state. For example, True/False isn't a bad option, the answer should be of course entirely true or false, and just don't use too many. One common pitfall of TF, MC and some others is they test "recognition", not "recall" -- the correct choice is presumably present. For recall, try short answer/fill-in's, or others.
My last nugget to share on quizzing generally is avoid these two pitfalls:
1) Questions aren't aligned to Objectives. You may be surprised, but suppose your course has 7 objectives. You'd better be checking the achievement of those. I've reviewed quizzes where not one question has been asked on one or more objectives. And have you weighted the number of questions on the most critical of them? One trick some designers do to get this right is as soon as objectives are nailed down, go right onto developing the assessment (before content development) while they're fresh in mind.
2) Question focus. Do they aim too low? Are they too easy or miss the point? This isn't to say they should be overly difficult either. The point is you generally should focus on the higher levels of learning and achievement, aligned with your objectives.
What do others think?