One of Jadeite's specialties is telekinesis, the power to move objects with the mind. He seems to be quite talented with this power, having both stopped Sailor Moon's tiara in flight, and then there's of course those jets.
The second power he has, and maybe the most notable, is the ability to create elaborate illusions. Jadeite can become virtually anyone, and even after the senshi meet him several times they are unable to recognize him. He can also create false materia, like most of his shops and the castle in the Dreamland amusement park.
One of the most impressive shows of Jadeite's illusionary power was probably that time he let a huge image of himself be seen over Tokyo. He then proceeded to create the illusion of fire raging through the city to draw the Sailor senshi out.
I don't know if he could really make Tokyo burn, but I believe it's within his might. (Enough gasoline and I could do it. Bwahahahaha- *coughs* Gomen)
One thing that I find interesting is that Jadeite rarely wears "casual" clothes. When he changes his appearance, he often chooses a persona that is easily recognized and identified from the clothes. Like the time he went as a security-guard, or maybe the clearest example, as the captain of a ship. It might be that he is simply, after so many years as a Dark Kingdom commander, uncomfortable outside his uniform.
It could also be that since the knowledge of modern Earth doesn't seem too great in the Dark Kingdom (as shown when Jadeite explains how Japanese parents put their children through elite schools, and then finishes off with a 'I don't know' as Beryl wonder what happens afterwards) it's difficult for him to know how a normal human is supposed to look and act. So, he might find it simpler to dress up in a very stereotypical way, thus avoiding personal questions and inquiries about why he acts as he does.
By himself, or through his youma, Jadeite can drain humans of their life energy. The youma need an object of some sort (apple, disco-ball etc) to contain the energy. It appears that an item isn't necessary when Jadeite himself is stealing energy. Yet, he uses some kind of chambers to drain the girls trying to loose weight in episode four. My speculation is that the energy output is bigger if he has an object to focus on, but as one of the dark kings, he is strong enough to do without.
The longer Jadeite's youma can work without interference, the more energy they transmit to him, but the risk for the victim's death also increases. If the focal-object or the youma is destroyed, the energy they've passed on to Jadeite dissolves, unless he's had time to feed it into some kind of container (so why can't he do that more often? Jeddy no baka).
Once someone has been drained, they become easily influenced by outside powers, such as mind-control.
It appears that Jadeite can drain larger amounts of energy faster then his youma can, as shown in ep. 13 where he puts an entire police squad out of commission. But, since he is a high ranking commander, he probably feels it is under his dignity to go and to the dirty-work himself. It might also arouse too much suspicion if large groups of people simply collapsed within seconds of his appearance.
He also has the standard 'blast of energy', in form of pink lightning and can create mud-demons which look human to the eye. Other powers is the ability to levitate, clearly shown in several episodes, as well as an ability to stay longer then humanly possible under water. He was glowing when he came up, so he might have created a force-field around him while under the surface.
I don't know if this counts as a power or not, but he is shown holding a sword and a shield (the ep. where Kunzite dies) and it's safe to assume he can use both. It is unknown if Jadeite handles other weapons as well, or of what type those might be.
Finally, Jeddy has some very nice ways of teleporting. Rather then simply fade away, or disappear in colored light as the other Shitennou, he often uses black portals of some kind. They are very alike the gates that lead from the Earth in to the Dark Kingdom in look. This does not mean he isn't capable of vanishing in thin air, but I like to think his sense of drama makes him do it with some style, when given a choice.
Anime - Which magic is used in which episode?