It may be that whatever the disadvantages of being left-handed, there may be compensating advantages.
Good point, moss. I found this--a set of test answers--that gives a concise summary (though I doubt that it's complete).

Faces=right-brain behavior; Names=left-brain behavior

Spontaneous=right-brain behavior; Organized=left-brain behavior

Fantasy=right-brain behavior; Realistic=left-brain behavior

Intuition=right-brain behavior; Logic=left-brain behavior

Open-ended=right-brain behavior; Well-structured=left-brain behavior

Pictures=right-brain behavior; Language=left-brain behavior

Creative=right-brain behavior; Not creative=left brain behavior

Humorous=right-brain behavior; Serious=left-brain behavior

Main idea and overview=right-brain behavior; Details and facts=left-brain behavior

Exploration=right-brain behavior; Systematic plans=left-brain behavior.
http://www.education-world.com/a_lesson/TM/WS_brain_key.shtml

Hey, this is really cool! Esp. take a look at 'Warnings'.
Introduction
Some language skills involve analytical, sequential, and left-brain processing. Others involve right-brain skills such as guessing, associating, and getting the main idea.

Obviously, those with bilateral dominance have some advantages.

There are, however, good language learners with both left-brain or right-brain dominance who achieve a high degree of fluency and accuracy. They learn to use both left-brain and right-brain skills depending on what works best for the activity at hand.

Guidelines
Here are some general guidelines to follow when you use your brain dominance for language learning:

Use your left-brain analytical skills to determine the purpose of a learning activity or to set up the activity. Once you are involved in the activity, put most of your attention on the content of the message and let your right-brain go to work.
According to James Asher, author of the Total Physical Response method, direct association methods for building listening comprehension rely more on right-brain processing than on left brain processing. Do not consciously try to figure out every detail when using these methods. Let your subconscious do the work.

Warnings
Here are some warnings about using your brain dominance for language learning:

Analytical thinkers who make good linguists sometimes never acquire communicative fluency in a second language because their left-brain, sequential processing slows them down.
Right-brained, global thinkers sometimes become quite fluent in comprehending and expressing themselves in a second language, but never become truly accurate. They are content to get across the main idea without worrying about the details.
You can read more by going to
http://makeashorterlink.com/?W25E12566