I have a very strong "handedness" preference, but it varies by the nature of the activity. For example, I write and throw almost exclusively right-handed, but eat (when not using a knife) and use the computer's mouse from the left side (which many people find kind of weird). My left eye is decidedly weaker than my right - if I cover my left eye, all I lose is a little peripheral vision; if I cover my right eye, I can barely see.
Not surprisingly, I have very noticeable problems with fine motor coordination, particularly when bilateral. Even fastening buttons is a major struggle. I am equally non-adept at gross motor activity, aided by terrible proprioception - walking into things is a multiple-times-daily occurrence.
Incidentally, I also have difficulty, quite pronounced at times, organising the avalanche of thoughts tumbling about in my mind. Organising even a simple set of actions, such as preparing a meal, requires intense concentration. I need to think and do things in my own way, and at my own pace.