It absolutely depends on jurisdiction, to my knowledge these laws are usually (always?) state-level. In my state, North Carolina, an "exact speed limit" state, for years the law was that if you were clocked less than 10mph over or under the speed limit, you were ostensibly traveling at exactly the legal limit, because police radar could legally only measure within +/- 10mph of the actual speed at which a vehicle was moving.
(This was, historically, due to federal legislation that mandated a maximum highway speed limit of 55mph in order for a state to secure federal highway funding. The state legislature complied with these regulations without compromising their constituents' ability to drive at 65mph by posting a 55mph limit and allowing motorists to travel 10mph over the posted limit. Those federal restrictions have since been lifted.)
Recently, a new party was voted into control of the state legislature, and the law was changed -- police radar is now legally exact to within 1mph, and a driver is in violation if they don't travel the exact speed limit on a given roadway. In practice, however, motorists found in violation can often plead guilty to a lesser charge -- that is, to a charge of "improper equipment" -- so the prosecution can avoid the costs they would otherwise incur by actually having to prove their case. This doesn't apply to severe violations, like going 90mph on a freeway marked 65mph or 55mph in a 35mph zone, which are often criminal misdemeanors, not traffic citations. In general, whether someone is eligible for such a reduced charge depends on their history of traffic citations and on the local district attorney's office and the presiding judge.
Some other states do not have an "exact speed limit" and drivers are responsible for maintaining a posted minimum speed (where applicable) and not exceeding a posted maximum speed. In these states, minimum speeds are often present on interstates and other major divided highways and often absent elsewhere. Where in doubt, follow the speed of traffic or stay 5mph under the posted speed limit, as indicated by your perhaps glitchy speedometer.
To answer your question explicitly, and in general, yes, as an auto registrant you are responsible for keeping your automobile in good working condition. However, there are often charges less costly than exceeding a posted speed limit for which you can accept a plea bargain or for which you can provide evidence to the court to reduce your responsibility.
(My source is personal knowledge and experience as a licensed driver in NC)