For any topic, issue, circumstance, etc. that is the source of an academic discussion/argument/debate it is vital that all parties involved recognize and respect the varying viewpoints of those participating in the 'argument'. This means that it should never turn into a mud-slinging event. In addition, depending upon the topic a good argument should always include valid data, several primary as well as secondary source material, experts to interpret any information used in the argument (from both sides). Lastly, it is extremely important for those involved to agree to a 'follow-up' session. It allows the individuals time to internalize their opposition in an effort to either strengthen their original position, defer, or concur with other positions within the argument.
One of the greatest difficulties in participating in an argument is facing someone who adopts the attitude of "my mind is made up; don't confuse me with facts." When someone is unaware of the factual grounds to support their side of the argument and is unwilling to give any consideration to any facts presented by the other side, the argument deteriorates into pointlessness quickly.
I have to agree that an argument must be grounded in differing of individual understandings. People will not argue if they see eye-to-eye on a subject. Therefore, people must simply have different points of view about a subject and the belief that their position is correct.
A good argument needs to have solid, provable evidence for support. As one creates an argument it is vital to be aware of common fallacies in reasoning. Be sure to read-up on the topic fallacies and understand how they occur. Once you know that you are not using fallacy in your argument, then make sure that you explain WHY your evidence is good evidence. It is not up to your audience to make the connection, you must do it. Sometimes writers think that the reasoning is "obvious," but even if it is, it should be explained. As you write, ask your self "why" and then WRITE the answer to that question as part of your argument. It will create a much stronger stance overall.
I think one thing that greatly weakens arguments is if they fail to anticipate the arguments against those arguments and find a counter-argument against them. If an argument fails to take into consideration points against it, it will ultimately be rather a weak argument.
The "Frame" of an argument is key. It's a tacit (or explicit) understanding between parties regarding the scope of the argument, which implies a common understanding of terms and facts. Sometimes there's a "preargument" regarding terms and facts, so the real argument never gets argued, or worse, parties argue the preargument but think they're arguing the argument!
One common flaw in argument is a confusion between correlation and causation. For example, I might say that all people who smoke marijuana will die. Aside from the fact that everyone will die, with or without having smoked marijuana, that is a flawed argument because there is a correlation between smoking marijuana and dying, but that is not the same as demonstrating that marijuana causes death.
It's hard to say what grounds an argument needs to have without knowing what the argument is. If we are told what the argument is, we can know what grounds would need to be presented in order to prove the argument. For example, if we want to argue that marijuana is worse for people than alcohol, we would need to find grounds that demonstrate things like how addictive each of these substances is.
The "grounds" of an argument are basically the data or facts that support the argument. Such "grounds" would be unacceptable if they were (among other flaws) untrue, false, incomplete, rooted in bias, or highly debatable. For example, if I provided inaccurate or outdated statistics to support an argument, the grounds of my argument would be faulty.