How to rehab a weed infested lawn

All this snow has got me thinking about spring, but the weeds seem to be making their way to the front of my mind.

First the specs:

• I live in Massachusetts, and the lawn is mostly Fescue/KBG.
• About 1.5 acres of property, all lawn minus a few decorative trees and flower beds, and the footprint of the house and driveway.
• Mountain of thatch removed in Spring 2013.
• Soil sample taken in Spring 2013 revealed the need for lime.
• Treated with lime and Scotts +Halts in Spring 2013, and Lesco Summer fertilizer in Summer. Stopped treatment of the back and sides as I felt it was a waste of $$ and more serious action was needed, where the weeds are worst.
• Extremely bumpy lawn, which I was told was caused by moles. Flattened out over time with weekly poundings from the tractor. Now bumpy again in mid-winter since mowings stopped in October.
• Weeds include large patches of red, stringy plants, cabbage-looking plants, and one particularly hard-wooded plant that got its head chopped off weekly so I wasn't able to identify it (the 'stump' of this particular weed is very woody and has multiple shoots), and the usual host of all sorts of other weeds. I'll see if I can find up some pictures.

And now a little backstory...

My wife and I bought our house in Winter 2012 from some folks who neglected the lawn the last year they were living here. We decided to let the year run it's course to see what the property would look like throughout the seasons, with only regular maintenance (fert. and mowings). Overall, the lawn was very nice/thick/healthy in the front (where it counts!) and absolutely terrible on the sides and in the back. The previous owners used to have dogs that they'd let pee all over the yard, so guessing that was what killed the grass and made room for all the weeds.

In the spring and fall, I bagged clippings after mowing, and mulched them during the summer. The lawn is also fully irrigated and received a thorough soaking (about 1" of water) once a week. After a few weeks, I limited waterings to the front only as I didn't want to help the weeds.

My question is then, what's the best way to overhaul large areas of lawn? I know the best time to plant grass is in the fall, but was hoping to start rehabilitating the lawn this spring. Also, I feel like I should maybe rototill the large trouble spots and seed over that. I would be willing to apply a weed killer, but since it's such a large area I'm not sure that would make sense. And lastly, I saw someone last year burning areas of their lawn in the spring, and it came back beautifully after reseeding it. Would this be a better option than tilling?

Thanks!