From what I've read, twice a week is sometimes needed during the prime growing season, especially with lots of rain. As far as the random sprig, is it near the edge of the mower, or in the middle?

My mower leaves random sprigs, too. I believe it has to do with the speed of the blade. I have a Black & Decker battery powered mower that has never been quite as good as a gas mower.

If you are mowing at the highest setting on your mower, the grass can get pretty high before you need to mow it again. It does not grow any faster when it is tall. A byproduct of tall grass is deeper roots and it uses less water.

If you mow it at 2 inches and it grows 1 inch per week, then you are clipping 1/2 of the grass off. If you mow it at 5 inches and clip back to 4 inches, then you are only removing 1/5 of the blades.