The world is flat, if you don’t look too exactly. When people generally lived in small communities, city states or small kingdoms consisting of a few villages, there was nothing irrational in assuming a flat world. The theory of a spherical world only emerged much later, when states like the Persian or the Roman Empire stretched over larger parts of the globe.
Be it you apartment, your garden, or your neighborhood, for most everyday practical purposes, you can pretend as if Earth is flat. The maps of the land-registry showing borders between estates treat the land as flat. On these small scales, the errors made by ignoring the more or less spherical shape of earth are negligible and probably smaller than the inaccuracies the maps have anyway. Treating Earth as a sphere would, on this scale, only complicate things without giving you any advantage. As a result, we use a theoretical framework that we know is wrong in a strict sense, because it is useful.
Increase the scale, though, and the errors become larger and larger. For a small country like Liechtenstein it might still suffice (I have once been there – standing at the Rhine river on the Switzerland side, you can see both ends of that little country if you only turn your head) but take something the size of Germany or even the USA and the mistakes would become so large you can no longer ignore them. If you fly by plane from New York to San Francisco, using the flat Earth model would lead you anywhere but not to the airport you want to reach.
On the scale of the Earth, you can treat space as Euclidian and use the laws of Newton’s mechanics, even if we know that, strictly speaking, they are also wrong. Space is warped. On larger scales or when you calculate the movement of something very fast or when you use very exact clocks, you have to use general relativity instead. For example, the satellites of the GPS system, used by many now every day to navigate around when driving car, contain very accurate clocks. In order to provide accurate positioning and navigation, calculation procedures derived from general relativity have to be used.
These examples show that for different purposes, you may use different theories. By increasing the exactness of measurements, the interface with reality is widened. Theories that worked while using a narrower interface with reality and are still useful as long as you stay inside that narrow neighborhood run into anomalies when more information is taken into account.
Such theories may be viewed as analytical spaces that contain a limited amount of knowledge about some aspects of reality, have a limited area of applicability, and have anomalies at their borders. As long as you treat such theories as models of reality that do not claim to be true, but are useful for certain purposes and within certain limits, there is nothing wrong with them, as long as you know they are limited as-if-constructions and you know when to switch to another one.
Problems start when you declare such a limited model to be the truth. You can do so, but then you have to find ways to ignore the evidence against it. You can literally ignore the counter-evidence, tell lies, lock the evidence away, ban it, put books and publications on an index, prohibit free discussion and exchange of ideas, threaten, lock away, torture or kill proponents of other theories. You can form closed communities in which people confirm to each other that earth is flat (or whatever the content of the theory may be). You will live inside an as-if-construction that claims not to be one. We call this ideology or dogmatism. People deceive themselves this way or they are deceived by others because ideologies are the tool of choice to exert power and exploit people.
A living organism can be viewed as the implementation of a more or less simple theory about reality. As long as it stays inside the scope of usefulness of that theory, it will survive. If it moves out of it, it will die. A species that moves out of the scope of applicability of the knowledge it encodes will go extinct. Humans are not exempt from this. Most of the information we are using is no longer the information encoded in our genes but the information encoded in our books and computers. This information encodes theories about reality that our civilization holds. If these theories are wrong our civilization is in the danger of collapsing, and our species (along with many others that are affected by our actions) is in danger of going extinct, like many species before it.
Therefore, instead of cocooning ourselves inside religious or political ideologies, inside a soft silken cushion against reality, we better try to smash our theories against reality as hard as we can to see if they break.
About the pictures: The first picture, from http://en.wikipedia.org/wiki/File:Baylonianmaps.JPG shows what might be the oldest known world map. Based on the amount of knowledge available at the time and the width of the interface Babylonians had with reality, this model might be viewed as scientific. This is not true, however, for the map depicted in the second picture.
The second pictutre (from http://en.wikipedia.org/wiki/File:Orlando-Ferguson-flat-earth-map_edit.jpg) shows a non-globe model of the earth from the 19th century, based on a fundamentalist, that is, ideological, interpretation of the bible.