Believe it or not, if you wipe down any stainless steel surface with the Financial Times you'll find that all smears will disappear. It's actually a top tip I was given by my husband! He used to work in a fish'n'chips shop and said that they always used the FT to remove smears. It's something to do with the ink used in the print. It works too. Brilliant.
After cleaning wipe over with the barest hint of baby oil and buff up. Also use this on the plastic top of my water jug, to remove the water stains and slate table mats.
Get "Bar Keepers Friend". Find it online or at your local gocery store. I found it at my grocery store. www.barkeepersfriend.com.
The powder works well for harder stains, but for stainless steel cookware I recommend the liquid. It cleaned my pans back to sparkling new!!! Got rid of that yellow tinge and the over spray that bakes on when oils and such splatter and get on areas not covered by teflon. Its FABULOUS! As long as you follow the directions the liquid did not scratch my my stainless steel cookware.
DO FOLLOW the directions well. I get the pan wet, get a 3M O-Cello non scratching scurbby sponge wet and put the liquid on the sponge and buff. For harder stains you may need to use the powder.
I use powder for my sink and liquid on my pans.
After cleaning I always found smears and water marks on the hob, door etc however much I "buffed" the damn thing! The best best solution I found is after cleaning rub in petroleum jelly with a kitchen tissue and voila!! No smears it really works!
Buy an E-Cloth from B&Q or off the net, it's a cloth with really fine fibres that cleans up stainless steel/glass like a treat!
Just wipe away all the grease using Jif (or Cif or whatever it's called), get your E Cloth (no need to moisten) and gently wipe over the whole area!
It's a lifesaver and can be washed and reused! It's great for mirrors, hobs, high gloss cupboards... I'd marry that cloth if I could!