I've been studying Wado Ryu Karate for 13+ years starting at age 7 in the UK. I have supplemented classes with reading and research in books and on the web, and have developed a perfectionist attitude to the form and practise of Karate. I currently hold the Nidan black belt grade (2nd Dan) and am a judge in Kata competitions and tournaments within the small company I am affiliated with. Prior to becoming a Kata judge I competed in a number of Kata competitions within the company and attained a 100% 1st prize record. However I certainly don't consider myself any kind of authority on Karate or Kata, I have simply found that the following guidelines have served me well and assist the students I teach in improving their Kata particularly in preparation for performances or competitions.

The following 5 guidelines seem to be relevant to most forms of Karate Katas I have seen, however my range of experience is limited, so treat these as guidelines not rules or anything like that. Some of this will only make sense to practitioners of martial arts or Karate.

(1) Every move has a stance.
Stance defines the base position of the body and limbs. In Karate there are a great many stances offering different amounts of stability, ease of advancing movment, ease of retreating movement, and so on. It is from the base of a stance that moves are performed, moves being punches, kicks, blocks, preparatory movements and so on. A Kata is made up of discrete moves from the full repertoire of the Karate system. You must know what stance a move is based in, and you must be able to form that stance perfectly. If you cannot, then you must practice it until you can, as stances are one of the most fundamental building blocks of Karate as to be totally essential in performing a Kata well. If you do not know what stance a move is, then try to work it out. Certain moves make more sense in certain stances. Failing that, just choose a sensible one and form it properly until you can find a reliable source to set you straight. Never form a half-and-half stance. Do not try to hedge your bets! The wrong stance performed correctly looks 100 times better than no stance at all.

(2) Separate the moves.
Finish each move before you begin the next one. Do not rush. Each move should be performed individually, paying attention not just to where you end up, but how you get there, and what sub-moves (eg 'reactions') you perform on the way. Sub-moves too must be discrete (separate) and must not run into each other. Note that there are sometimes parts of Kata which might seem to break this rule - several seemingly independant moves are performed without pause, or even simultaneously. These moves are still performed under control however, and you should always complete a move before starting the next, even if you do so very quickly and without a pause in between (such as with a double punch for example). Never ever half-do a move. A punch that aborts halfway (or worse, trails into the next movement for no apparent reason) isn't worth the wasted energy. Moves performed simultaneously are either done so because extra power is gained in this way or perhaps because it is in fact a single move that you have not been taught before. Much modern martial arts teaching has been watered down over the years due to increasing commercialisation or the splintering of instructors from their own sensais (where the link to further knowledge is effectively severed). In this way moves and ideas are forgotten and yet retained in the movements of the Katas. However you can be sure that in its original form the moves in a Kata all had a base in real techniques.

(3) Watch the ghosts.
Every move is directed to parry an attack from an unseen opponent, or to strike him. You must watch this imaginary opponent (ie ghost) at all times. Kata are frequently performed against several of these ghosts, who are spaced all around you, watch each one just before you move against him, and also whilst you do so. If you need to turn to face another direction, then before you move from the previous stance, turn your head and eyes and look at the next ghost. Note, I say look at them, ie actually try to focus on someone who is not there, do not simply turn your head in the right direction and look at the wall. This is an excercise in imagination! It should be possible to perform a Kata as perfectly with your eyes closed as it is with your eyes open, as you are moving in response to predefined imaginary stimuli but watching your invisible opponents gives you a better sense of the flow of the Kata and what it says about real-world application of the moves. I teach my students that the correct way to go from one move to the next goes in the order eyes (if there's a change in direction), legs (or stance), arms (or the actual move itself). For example to move from a left shutouke (knife hand block) in mahanmi no kokutsudachi (a long back stance) to a sotouke (outer forearm block) in mashomen no nekoashi (short front facing 'cat' stance) 90° to the right you should first turn the head and look where you will be going. Visualise the incoming attack (perhaps a junzuki punch to the body or some similar straight punch). Then move the legs, and then position the arms*. Putting the movements in perspective like this not only improves the look of the Kata but also improves your Karate.

(4) Stay in control.
Just as every move has a stance, every move also defines exactly where each part of your body should be. You should always know where your arms are, what your hands are doing, (open? closed?), where you should be looking (see 3), how your hips and shoulders are facing and so on. You must stay in control of your whole body, not letting anything go. At the highest level Karateka train to remove all unnecessary movement from their actions so as to make the moves as effortless and efficient as possible. This is why ancient grandmasters can still kick the asses of fresh young upstarts late into their dotage (well legend has it anyway). This level of control is related to the concept of kime.

(5) Anger!!!
Karate is definitely not dancing. And although much Karate taught nowadays is sport, Kata pre-date that. Kata are a traditional expression of Deadly Force. The moves are designed to wind, crush, break, rip, and kill. It is neither funny nor embarassing. A Karate Kata must be all or nothing. Either you make it look like it matters or you don't do it at all. This means that you must put some force behind your punches and strikes. Your kicks have to be precise and strong. You must block fast and hard, and almost every move should lock under tension when finished. Kiais must be not just loud, but powerful. Don't smile. Definitely don't laugh. When performing a Kata you should express yourself as you would in combat.

Aside from above the 5 guidelines above, the best way to improve the look of your Kata is to practice the moves themselves. Practice stepping punches (Junzuki, Gyakuzuki), and blocks, and difficult stances. Practice moving from one stance to another, especially the awkward and powerful transitions such as Nekoashi to Zenkutsudachi etc.
To improve your memory of a Kata, break it up into sections and practice them repeatedly. Take care when breaking up a Kata so as to preserve sections that are clearly part of a short sequence such as a sustained attack or block-retaliate pairs etc. A good teacher will be able to assist you with this. Once you have memorised these sequences, practice the sequences in pairs and triplets so as to strengthen the links between them (so you don't forget what sequence comes next). When practising Kata you should frequently start facing in a different direction so as to prevent you from picking up cues from your surroundings and effectively tying your performance of a Kata to a particular room.
You need to be physically fit to perform a Kata well. Kata must be performed with a lot of energy, and sustaining this level of output, particularly towards the end of a long Kata, can be very physically demanding.
As a final point, try to think about the moves of a Kata with regard to their real-world application. Consider what you can learn from the Kata. If you cannot come up with some ideas why certain moves are the way they are or why you turn in a particular way or whatever then ask someone, or do a little research. Most styles have a guide book, and if the upper echelons of your organisation and its doctrine do not have the answers then find out what your style was based on and research its origins. Many of the different flavours of Karate come from different peoples' takes on their art. Some moves are the result of misunderstandings or the gradual loss of knowledge. Others are due to new innovations. The study of Karate and indeed all martial arts is only maybe 30% physical. To truly excel one must study both intellectual aspects of the system such as the physical and biological concepts upon which moves are based, and the artistic and philosophical aspects such as kime, kiai, chi and so on.

*OK I chose a bad example here. This movement is actually rather complex. In virtually all cases there is the requirement for arms and legs to move in concert to reach the final form of a move. This is because the power, speed, balance or whatever of the move lies in a clever marriage of opposing forces and momenta (momentums?). In the example given it would be my guess that the front leg would come back towards the back one and form a temporary mashomen no nekoashi with the shoulders and hips moving to face the target of the original shutouke with a preparation/reaction movement of the arms (the right held horizontally low across the stomach and the left in a covering position with the fist near the right shoulder), and then a sharp twist as the legs switch over to form the right mashomen no nekoashi and the left arm pull down to the hip and the right rotate with the body rotation to the outer block position, but there's probably a million different ways of doing this one movement. Trust me to pick a tricky one :)