I have a 2002 Honda Civic Ex. I've noticed about 10 times in the past 5 years of driving this car that the speedometer instantly drops about 10 mph, and then resumes normal operation. A new problem this year is that the odometer light is not working. Is this a sign of something that needs to be fixed (before something else breaks)?

Have your trusted mechanic look at this for you as you do not want this light to go out while driving at night, nor do you not need to know how fast you are going. There is definitely something loose or the speedometer is going to stop working altogether soon.