If the spots you are have problems with is where the dog is doing his business all the time you will not be able to keep a good stand of grass. If that is not the case, is this a really shaded spot? If so you need to use a grass seed that is made just for shade. Make sure that it is NOT annual rye grass seed because that is not a good seed. It is an annual seed.
If it is right out in the sun and you can't get a good stand of grass I recommend calling a lawn expert. You may have grubs or some other kind of boring bug that is preventing your lawn from growing.
Our lawn is about a 1/3 shade and it is very hard to get grass growing. In one area beside our house we decided to put a flowered walk area filled with shade plants because we could not get grass to grow and our lawn man said it is the cheapest way to cure the problem. It was an area where almost no direct sun light gets to because of the trees. I love my shade garden.
Back to your problem. We have a lawn service that comes in 5 times a years to fertilize, put down weed preventative and aerate our yard. They also do grub service upon request. Having your yard aerated at that beginning of the season is very important. It always the grass to loosen up and water and fertilizer to go directly to the roots. If you do not wish to hirer some one you can rent a unit and do it your self but it only cost us $49. for a lawn less than 5000 sq feet. If you have never seen an aerated lawn, what the machine does is rolls over your lawn taking small plugs of your lawn up. When they are done my son says it look like a bunch of raccoons used are lawn for there bathroom. Don't ask me why he says this, he is 17 years old and teenagers mind work different than ours.
Getting rid of all the crab grass and creeping charlie, etc. is very important to a health lawn. Creeping weeds strangle your good lawn and it takes over. If you do not wish to hire some one to put down the fertilizer/weed killer, I recommend using Scotts or Weed and Feed. These can be bought at Farm and Fleet, Menards, Wal-Mart, etc. But you really have to aerate your lawn to make sure the fertilizer and weed killer are getting to were it needs to go. You also need to apply these product when the dew is still on the ground or right before the sun comes up. You will need a spreader for this.
I hope that some of this advice will help you. Keeping a great lawn is a lot of work. That is why we decided to hire a service. It costs us less than $200. per year for 5 lawn treatment and an aeration. It really save use on headaches but there is still those couple spots where it was just better to plant some ferns, sweet william and some hostas because grass was not going to grow where the sun don't shine.
Good Luck and may your lawn soon be very green.
S.