Practicality of attaining a law degree despite difficulty remembering facts?
How well do you remember films? 

I had a similar problem, though not as bad as you describe. I found it helpful to think of each seminal case as an old black-and-white movie with a dramatic scene as judge's read their verdicts. I forget dates, but I remember the meanings and that proved much more important. 

Side note: A law degree is (typically) a very field-specific endeavor. If you have a good reason to pursue it, then I wish you the best. But, just in case you've never heard this before: unless you plan to practice law somewhere, law school probably doesn't make good sense.