I am SO glad you wrote in before you did any of the things you said. Too many times someone writes in second guessing something they already did and it's a disaster.

In your case, OVERSEEDING would be the disaster. DO NOT OVERSEED into a sodded type of bermuda lawn. NEVER, EVER do that. Sodded bermuda is a different type of plant than seeded bermuda. It's like the difference between a chihuahua and a great dane. Both are dogs but if you round a bunch of them up, it is easy to see which is which. Seeded bermuda is a weed in a sodded bermuda lawn.

Find the Bermuda Bible on the Internet. I would link you to it but GardenWeb won't allow that link (you'll find it on another lawn and forum website - long story). Memorize it. I will summarize for you so you can begin to think about the process.

Weekly - mow low 2 times and water deeply once
Monthly - fertilize with a high N fertilizer and water in

Details are in the BB

Note that herbicides are not mentioned. If you are doing those things, you should not have any weeds. If you get some broadleaf weeds after a month of following the BB, then spot spray with Weed-B-Gone Clover, Chickweed, and Oxalis spray. The secret to no weeds is allowing the soil surface to dry out completely before watering again. In the spring that means watering only once every 3 weeks. As it warms up toward May, move to once every 2 weeks. With temps above 90 degrees, move to once per week watering. Weed seeds must have continual moisture for days to germinate. By withholding water, you break that cycle and prevent the weeds. Also the monthly heavy dose of fertilizer will keep the turf very dense and growing. That will help shade out any weeds that might get started.

It is likely your thin spots are in the shade (can you post a picture of the thin area?). Seeding new bermuda will haunt you. You will watch helplessly as the seeded stuff comes in nicely, then realizes it is in the shade and starts looking for the sunny part of the lawn. It will thin out in the shady area and absolutely ruin the rest of your lawn. What you can do in the shade is put in mulch, crushed stone, or some other permascape that will not compete with the bermuda.

Mondo grass is its own type of pest. Once you have it you have it for life. It spreads about as fast as glacier movement but it does definitely spread. Mondo grass is not a grass, by the way, so grass killers won't work on it. You can try RoundUp or Weed-B-Gone. You may end up digging up the entire bed to get the large, tuberous roots.

If you follow the BB religiously, you will have the nicest lawn on the block. If you want to further tune up your lawn, substitute at least one application of fertilizer with an application of alfalfa pellets at a rate of 20 pounds per 1,000 square feet. You can get alfalfa pellets (rabbit chow) at any feed store in 50-pound bags for about $12.50 to $15. Or you can apply alfalfa pellets in addition to the chemical fertilizer. The two types of fertilizer do not interact in any way. What the alfalfa does is improve the health of the microbes in the soil. The chemical fertilizers rely on having healthy microbes, but if you use chemical fertilizers exclusively, those microbes will become depleted. Using the occasional blast of real food (alfalfa is a food), will revive them and increase their population for the next dose of chemical fertilizer. When you apply alfalfa you have two more steps to make it work. First is to moisten the pellets so the birds don't carry them away. No need to flood them, just moisten them. When they get wet, about 12 hours later you will find them swollen and looking like green worms. Step 2 is to drag a hose, broom, or anything over the pellet worms to break them up and help them fall into the turf. Then the little flakes are invisible and down in the soil helping the microbes.

Here is a picture of seeded bermuda invading sodded bermuda. The clump is the seeded variety.

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Here is another in a different lawn.

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The second picture has a much healthier stand of sodded bermuda (Tiff 419 hybrid). The seeded bermuda has a lighter color, different growth habit, and is less dense than the Tiff hybrid. This owner made the mistake of not sodding all the way out to the curb which allowed the wild common bermuda to encroach.