(This is a bit of a condensed version of my post about the problems with dualism, to give you a quick and dirty explanation of dualism's problems.)
I am going to assume that you are a mainstream dualist: you believe that there is a metaphysical, thinking soul separate from the body that interacts with our bodies. This is your hypothesis. I am a monist - I believe that my body contains and generates all my mental processes. Normally if you have a hypothesis and if you are clever, there is a way to test it. I will play along that the soul is metaphysical and cannot be directly observed. Fear not, dear dualists. Many things in science cannot be directly observed by individuals - black holes, history, and the mind. But we can study thing we would anticipate around those unobservables - galaxies being sucked towards a single spot with black holes, buildings and documents with history. We can observe around the soul as well.
Your hypothesis is that the soul interacts with the body. We should be able to view this interaction, and this should be the focus of all of your research if you believe this to be true. There are many questions you, using science, should be researching to answer.
Where does the soul interact? The brain? Why the brain? Why not the muscles it wants to move? Is there something special about the brain? If not, why bother with the brain at all? Does the brain contain a soul-perceptive structure, or chemical? If so, we should be able to observe those chemicals or structures changing and moving with no discernable outside influence. If you believe in dualism, finding this chemical or structure is paramount. Once you have found it, you have to answer the question of why the soul limited to one person's specific brain. Why can't it influence other people's brains? Is the soul just very polite about controlling other people?
And then there is the problem of the body influencing the mind. Why do physical mind-altering substances (drugs), alter our minds? Not just drugs, but drugs that are able to move through the blood brain barrier frequently influences how our minds think. Why? Why would caffeine excite us? Or alcohol affect us? Why do we feel joy in the embrace of a loved one - an emotion that correlates to neural and chemical signals? Why are these earthly signals able to influence our thoughts? Does the body pass along these mental changes to the soul through the brain? If so, then we can exactly observe those signals that are sent along to the soul.
The body must collect and send its information with accordance to the laws of the physical world, and therefore to correctly interpret them the soul must collect them according to the rules limited by the brain. We should be able to see mental pathways leading to soul-sending sensitive areas or structures or chemicals - parts that the soul can interpret data from. (If the soul does not need a specific structure to read from, then what's the point of sending information to the brain in the first place?) Once the soul has received the information, the mental process pathway that informed it should not continue to fire, and especially not trigger a mental response such as a word or deed. If a continuous neural pathway can be show to have gathered the information and then sent back a reply, where did the soul come in? The soul needs to change or influence that pathway, and that should be demonstrable by any scientist to evidence the dualist hypothesis.
To the dualist who still believes that the mental processes happen all in the brain and are merely shuffled back and forth to the body through the brain - let me ask you this. What do you make of people who have had brain damage, who are left unable to remember, unable to form sentences, unable to see, unable to say nouns? What about those who are chemically depressed or unbalanced? Do you believe that there's nothing actually wrong with the mental abilities of the person, just something wrong with the soul's ability to interact?
Let us give you a thought-experiment. You are captured by psychopaths who have ensured you will never have contact with anyone else ever again. They offer you a choice - they will use anesthetic to remove either a limb of your body, or the forebrain (where cognition mostly occurs, removed in lobotomies). Would you allow them your brain, safe in the knowledge that your actual mind would be intact? You would not be interacting with anyone else in the future, so your ability to interact with them does not matter. It's just for your own mind. Or what if they offered you the choice between being torture you for a week, then killed vs. them just killing you right away? Would you choose death knowing that your mind would be intact and you would have spared yourself the torture? Indeed, if your mind remains intact, why bother with this life at all? Why not get to heaven sooner rather than later?
I realize that this is not as quick and dirty as I originally intended it to be upon its completion, but more of a re-hashing of all the problems faced with dualism. I am sorry, but it is quite an annoying thing and something that just needs to be approached logically and scientifically. If dualism were true, we would see these sorts of evidence for its existence. When you do apply a rigorous standard, however, the hope of dualism quickly crumbles just as any other fantasy. "Dualism" and "soul" are easy words to throw around, but what they actually imply is far greater, far more complex than anybody realizes when they say it. And far more unlikely too.