I know it has been a wet and colder spring, so didn't know if it's just taking a long time to green up, or if I need to start adding peat moss for TARR.

I'm seeing the same in my yard. When I pull at the grass it uproots easily.

This isn't take all,patch, it looks like winter damage. You should apply a good 18-6-12 Fertilizer with 40% slow release (Nitroform is good) at 1 pound actual N per 1000 sq ft. Slowly (Over the next 3-4 weeks) raise the mower deck to 4.5 inches and make sure it gets 1 inch of water per week. It will bounce back pretty quick, it is no different than St Augustine recovery from winter overseeding with rye grass.
To calculate application rates of Fert go here http://plantscience.psu.edu/research/centers/turf/extension/factsheets/calculations-turfgrass-fertilization

You may also want to remove some of the soil and mulch from the base of your Magnolia trees in the background, they don't do well at all with soil over their root flare.

And straighten out that pedestal thingy!

Don't forget the broken landscape light on the left and the swing set that needs to be staked down.

Thanks for the tips. I have since put down a heavy nitrogen fertilizer, so hopefully we will see some improvement in the coming days.