Vinegar eats grout, so don't use it on tile with grout. I've done that and I've had grout fall out in chunks. I even used a more dilute solution, and you could see that the grout was becoming worn away and it got more porous (which makes it easier for muck to get into).
If it's within the grout, baking soda and some tea tree oil should do the trick or you can use a spray bottle and mix some hot water with some oxygen bleach (which isn't bleach, it's sodium percarbonate and sodium carbonate, which make a reaction to form hydrogen - which blasts the stains away) and that gets my grout really shiny and white. It doesn't do much for the sealer line on the bottom of the tile - I pretty much stilll have to use Tilex for that sealant. The rest of my tub and grout is spanking clean with the OxiClean I use.