Cook spaghetti in boiling salted water according to package directions, adding fresh or frozen corn to the water for the last 3 minutes of cooking. If using fresh corn, use tongs to transfer ears of corn to a cutting board. Drain spaghetti. Rinse with cold water; drain again.
Cool ears of corn until easy to handle. Holding each ear at an angle, use a sharp knife to cut down the length of the corn cob, cutting off corn in planks.
In a large bowl combine spaghetti, cucumber, sweet pepper, zucchini, celery, and red onion.
For dressing, in a screw-top jar combine vinegar, oil, sugar, salt, dry mustard, and celery seeds. Cover and shake well. Pour dressing over spaghetti mixture; toss gently to coat. Gently fold in corn planks. If desired, cover and chill for up to 24 hours.