Does mowing the lawn fairly short help to get rid of coarse grass? Does it encourage bare patches?
Mowing too short will weaken grass and allows weeds, including coarser grass, to get a foothold. If you want to encourage good grass growth, it's better to mow regualrly but not take too much off.
Bare patches can be caused by uneven ground, or areas which are a bit inhospitable for grass to thrive - ie shade, compacted or waterlogged ground, or a combination of those.
How you deal with coarse grass depends on whether or not you use a chemical or organic approach, and also how much the coarser grass bothers you to start with
Agreed with Fairygirl.
Mowing too short will weaken the lawn immensely, leading to dying grass and moss and weed issues.
Some types of coarse grass can be dug out with a dandelion fulcrum if you'd prefer a non-chemical approach. Pics of affected areas would help identify which type of grass is the issue and what method of control would be best.
As this growing season has been incredibly dry for much of the country, cutting it short may kill the good grass very quickly especially if the soil is dry.