So I've read a bit about them.  Do you worry about it or just run?  My run this morning I did 5 miles and my 4th mile was my fastest ever at 12:50 (please don't laugh) and I felt good at the end, tired but good.  So are negative splits something I should work towards or just really not think about it at all?

depends on the goal of the workout.  some workouts a negative split is great, other workouts like a long slow distance run and/or intervals, you may want to keep flat splits.  in my opinion, negative splits are great, but don't lay off in the early miles just to obtain negative splits, you should work hard (if the workout demands it) and strive for negative splits by putting yourself out there.

 I find that my first .5 mile is pretty slow as I have trouble getting up to speed and getting a good pace going, somewhere around .75 everything seems to go well, so pretty consistently my first mile is my slowest.  Does that sound typical?

yeah, that's typical. on long steady runs, if you wear a heart rate monitor, you may notice that your HR will rise quickly the first 1/2 mile or so, and then slightly come down as you settle in.