How important is the correct spelling of my legal name on a lease agreement?

Unless the name on the lease in question is totally different from your actual name, a minor variation (such as a spelling error) would not invalidate a lease. Frankly, typos happen all the time. For example, traffic tickets are notorious for misspellings, incorrect birth dates, etc. Yet they are still upheld. Bottom line, as long as you can reasonably be identified as the lessee, you are bound by this contract (which is what a lease is).