I noticed this on the window of a nice restaurant here in Winnipeg.
"Complimentary" means "provided at no cost," which I assume is what the proprietors of this restaurant mean.
"Complementary" means "goes together with, or completes, something else."
While you may feel wireless Internet service completes your pleasant dinner experience, this sign doesn't tell you the wireless Internet service is provided at no additional cost to you. To do that, it would need to say the restaurant offers complimentary wireless Internet service.
Think spelling errors don't matter to customers? Read this Shel Holtz article from PR Daily, "Spelling and grammar do matter, according to consumers," that suggests differently.