Don't worry about the mushrooms; they are simply a sign that fungal decomposers are hard at work. That's a good thing.

The same rules for all grasses apply to centipede. There is a direct corrolation between the blade length and the vigor of the root system. The higher the grass, the stronger and deeper the root system. If you mow on a regular basis (people tend to ignore their centipede), then there is NO reason why you can't have a nice looking lawn. Centipede responds beautifully to core aeration, de-thatching, iron applications, etc. Don't go overboard with the N.

My backyard is filling up with mushrooms. What can I do?

I find that a 9 iron takes care of them pretty well. You could also try a sand wedge.

I have been told to cut the centipede pretty short. Will it ever be possible to get a nice plush lawn with the centipede or am I doomed?

Your absolutely right, Centipede that is actively growing should be mowed every 7 to 14 days at 1.5 to 2 inches in height.

Yes, you can have a plush lawn. Established centipede lawns have very low fertility requirements. Centipede is low-maintenance and does not respond will to excessive use of fertilizer, especially nitrogen. Do not over fertilize with nitrogen. Fertilizer should be applied to centipede in 1 to 3 applications from spring green up through fall. Do not apply nitrogen too early in the growing season or subsequent frosts may damage the grass. Likewise, don't fertilize too late in the year, as this can slow regrowth the following spring.

Many thanks. I just mowed the lawn and it is looking so much better. The info that I have read on this forum and another forum on compost tea has made a tremendous difference. I have usually just cut the grass and forgot it.