As a parent or caregiver there is a great responsibility to start your children on the right path in life. To some parents it doesn't occur to them that teaching children to respect authority figures is one of the many lessons a child needs. Knowing how to show respect is not knowledge children are born with but a lesson they learn from birth as they watch the older children and adults in their lives interact with authority figures.
Children are sponges that absorb all that they see and hear. How you speak to your own parents and spouse (although your spouse is not your authority figure it is your child's) paves the way for how a child will speak to these same people. If you are rude, sarcastic or speak to other adults with rolling eyes, huffy voice and exaggerated “put upon” body language chances are your child is going to pick up on this and use these same mannerisms with the adults they encounter. It can be hard for adults to change behavior they have been accustomed to but once your child deals with you the same way they have seen you deal disrespectfully with other adults (whether you realized you were doing it or not) it will open your eyes.
Remember the first teacher in your child's life is you. How you feel about authority figures, how you talk about authority figures including police, firefighters or your own boss at work will all be absorbed by your child. How you speak about these officials, which have authority over society or your job, teaches your child that you either respect these individuals or you don't. If they hear you speak disrespectfully about these individuals your child will learn it is okay to speak badly about them or treat them poorly because they are undeserving of your respect. To truly teach children how to respect authority you must first model respect for authority.
Police and firefighters often have booths at fairs so the general public can ask them questions or sit inside a real fire truck. Take your children up to these authority figures and speak with them. Allow your child to see you interact with the individual with mutual respect. If you happen to be pulled over by a police officer and receive a ticket, whether or not your child was in the vehicle at the time, don't bad mouth the police officer for doing their job. You may not feel like thanking the police person but it would be a good show of respect for the authority the police have over the safety of the roads and a way to take ownership of your own mistake.
In school the faculty are like bosses to your child. The teacher sets goals and deadlines that must be met and although most of us don't view school as a job it is for your child. If you have a problem with the teacher or other faculty members it would be better for both your relationship with your child (who may actually like these adults) and the relationship you have with the faculty member to not speak disrespectfully about them in front of your child. If you do you damage three relationships, the one you have with the school, the one you have with your child and the one between the school and your child.
Respect for authority, when taught from the start, is not a hard lesson for a child to learn. For older children it can take a little more time and adjustment from you to ensure they have a healthy respect for authority. With time and patience you will have the success you seek.