Shots
The very basic mechanic of a shmup is the shot. I can not come up with any shoot'em up which does not have shots in it. Therefore these game elements have to be designed very well. I'm going to explain each design aspect for them as far as I figured them out.
Size
Visibility and difficulty are bound to the size of shots. The more space they occupy the less space is left for dodging them. There are even weapons like ray guns which create an insuperable barrier which cuts the play field into halves. Making shots too small is bad design and will frustrate players because small sprites are more likely to be overseen. Big shot sprites are not that bad but may become hated when they go beyond useful limits.
Speed
Fast velocities decrease the time frame for figuring out how to dodge shots. It's a screw for tweaking the difficulty level. Speed may also accelerate over time, e.g. for heavy ammunition like rockets leaving their launchers.
Shape
Most shmups use abstract shapes like circles, ellipses, lasers or flares for their shots. Sci-fi is well suited for these shapes. Exceptions like Battle Garegga or Progear use more authentic shots like bullets or rockets to support the mechanical steampunk flair.
Shapes also may support fast identification of behaviour. E.g. missile-shaped shots are often expected to be target-seeking.
Color
Many shmups use glaring colors to make shots standing out against other sprites like enemies or background graphics. Colors can also be used for giving clues about the impact damage or behaviour of shots.
Movement
Most shots travel on a straight line with constant velocity. In this case dodging strategies can be figured out easily (simple to figure out but hard to master in real-time). Non-linear movement makes staying alive harder. You can try out complex bullet patterns here.
Nordenfelt, Shot Type 1
The first shot type I've created for Nordenfelt is a flare. Flares have good visibility, are abstract and therefore scalable without losing their authenticity:
One interesting note here is that the trailing smoke effect breathes life into the game. The game its soul starts to unfold. It seems I'm on the right way.
Cheers,
Thomas