Well, if you are going for the dig it out method, I wouldn't leave any bald spots sitting around. You'd be amazed how fast weeds can fill in bald spots. Get some grass seed. Dig out a patch of the weed grass, fill the hole with good enriched soil, water well, and plant that patch immediately! Then go on to the next patch. I know if your digging it all out project goes on for some weeks (it would if it were me!) your lawn will look a little patchy for awhile, with grass seed in all different stages of growing out. And if it is hot and dry now where you are, you will have to water the grass seed every day. But by next season it will be all evened out and you will have a lovely lawn for a little while
(weeds being pretty persistent and ubiquitous).
Or you can just decide it is all grass and keep it mowed. If it is all green and even height, it looks pretty much like lawn!