First and foremost is organization. If you have been cooking where you are for a while you should have your line set up the same way every day so you know EXACTLY where everything is. This will help with you forgetting random things. Just seeing the ingredient for a split second, if it is grouped with everything else in the dish, will hopefully remind you that "Oh yeh this goes in the dish too." If the menu changes, set up your line in a logical way, with the ingredients needed for the same dish located in the same area. I found this to be the best piece of advice given to me by a sous chef. You don't even need to think about where your hands are landing and can concentrate on more important things. This leads me to my second point:
Concentrate and focus on what you are doing and be aware. I know it seems obvious, but it is how you prevent mistakes. Be conscious of your movements and try not to waste motions. It makes it easier if your chef isnt a screaming maniac. (I don't know what the deal with screamers is, but thats a whole different thread). Being able to multi task is all about awareness - of your surroundings, of the smells and noises around you (if you have an excessively flatulent line mate this may make the smell awareness a little tough) and being able to prioritize rapidly.
Communicate with whoever else is on line with you. A smooth service is all about timing and getting those plates up without a whole lot of waiting on your fellow cooks or vice versa. Do what you can ahead of time - ex. when I used to work GM we did a lot of tartares and gravlaxes, so when an order came in for tartare I would plate it up and fire it in the low boy then wait until the dish was fired and I would garnish and send it up; if you're working the fryolator same deal - whenever an order for something like arancini or fries or something like that I would load up a basket and wait for the order to be fired then drop those badboys. Every second on the line counts.
Hope that helped a little and good luck.