Disrespect, be it from a stranger or a friend, has a way of stinging you to your core. It's especially bad when it is seemingly unprovoked. It's tricky to deal with, as the more mad you are about it, the less effective you will be able to deal with it. Sometimes simple provocation is the goal in and of itself by your antagonists. Thankfully there are a few universal ways to handle it no matter the specifics of the situation.
Use the golden rule in all aspects of your life. The better a person, friend, lover or coworker you are, the less validity other people's disrespect will have. Don't give others a reason to disrespect you. This is not a guarantee that it will never happen, but being the best you can be will make it easier to deal with if and when the situation arises.
Calmly let the others know how you feel. Their disrespect may or may not have been intentional, but you need to call them on it in a firm, polite and diplomatic manner, lest you bottle your anger up and live off of negative assumptions. You will find that more often than not, it was accidental. For example, if an employee fails to file a report properly, it's not as if she said "I really want to disrespect the boss by doing this." Chances are, it was garden-variety human error.
Avoid getting in an argument. Many times, mere provocation is the goal in and of itself. For example, a significant other may very well know that you are meticulous and thorough, but may decide to push your buttons by saying or implying that you aren't. If you delve into any semantics with him, it will be a losing battle, as he will only stick with statements designed to make you angrier, as opposed to those that have any truth to them.
Invite them to discuss the issue further at a relaxed, neutral location if you have regular contact with them. This won't work if it is a group of random strangers giving you disrespect, but if it's a family member, coworker --- anyone you see regularly --- hashing things out at another location at a separate time works well. This is because you have time to let your anger settle, in addition to the fact that a friendly public place, such as a coffee shop, may diffuse any defensiveness or confrontational notions.