I don't really use mayo, I prefer vinaigrette dressings. I was just using mayo as an example though, if you make mayonnaise yourself, it's just oil, egg yolk, and vinegar. There shouldn't be sugar in mayo.
On the second count, you're right that you don't need to be extremely strict. I went sugar-free for a month because I made a bet with a friend, rather than for any actual health reason. A small amount of sugar is fine for you.
The problem is that practically every shelf stable packaged food contains added sugar. If you have a diet that consists of a lot of packaged food, the sugar starts to add up quickly, especially if you're in a habit of using ketchup, which is astoundingly high in sugar. Granola bars (and granola in general) are also a food that people seem to forget contain a boatload of sugar too.