DO NOT TILL, just to follow up and agree with neliaz. If the contractors left your soil surface uneven, then the box blade is the universal solution. If you sod, you can do that any time from now on. If you decide to go with seed, wait until mid June. Bermuda seed needs hot soil (not hot air) to germinate. That would give you many more months to worry about erosion. Until then you can just mow the weeds and practice taking care of it like it was Buckingham Palace. Seeded bermuda and sodded bermuda are two different varieties of plant. They do not mix well in a yard, so think about that before you go buy any seed. Never seed bermuda to patch up a thin spot of hybrid (sod) bermuda.

If I understand correctly the grass looked fine for several weeks and suddenly got the various symptoms you described. Is that correct? You severely over watered for the first month and that is what led to the symptoms. The installer should have told you to water 3x per day for 10 minutes each time for the first 3-4 weeks or until the sod roots knit into to the underlying soil. Then start backing off on watering until you are watering every 5-7 days for about an hour. Even your nutgrass problem could be caused by the overwatering. It is a swamp grass and thrives with too much water. All the symptoms sound like fungal disease. The blob that looked like dog barf is commonly called dog barf fungus. It happens to be very ugly but it also happens to be harmless. You probably cannot really tell where that spot was several weeks later. The white stuff was likely powdery mildew. The blue areas were symptoms of not enough water but there are fungal diseases which cause the same symptom. The strong temptation is to add more water when that happens, but that is the wrong response. All the water goes to the fungus. How high/low are you mowing it? The installer should have also told you to mow at 4 inches (mower's highest setting). But this time of year is when you should be skipping mowing and letting the grass get up to 5 or 6 inches to endure the summer heat. Scalping fescue this time of year could be the problem for the large area that is dying. If you are mowing at less than 3 inches, then you cannot blame the installer for much of any of this.

Neither of those is really a good choice but if that is all the choice you have use the least expensive. What is your base soil? Putting a soil mix that drains very well on a clay base that does not can present problems not easily cure. As you have indicated the 50/50 soil/compost mix will shrink as the Soil Food Web digests that compost and your level lawn will no longer be level. A good soil will have about 5 to 8 percent organic matter in it which might be what that screened "topsoil" may have. Keep in miond that "topsoil" is quite simply the top 4 to 12 inches of soi from someplace and it might be something worth the price or it may not be worth anything.

Too late in the season to seed and expect any reasonable amount of germination. But you can sod right up until the ground freezes.....if you can find the sod (some sod farms stop selling this late) Just make sure you have the soil properly prepared first. Sod requires the same seedbed prep as seeding a new lawn would and since it is significantly more expensive than seeding, you want it to have the best possible chance. The alternative might be to seed with a cold weather cover crop to satisfy COO requirements and then seed your new turf grass lawn in spring.