Where flat earth is winning:
If you view far objects at far distances (ie, lighthouses 100 miles away) distances, this seems to point to earth being flat. Round earth counter-argues this with light refraction argument - I don't buy this argument, because light refraction is only caused when light enters a new medium such as from air to water. I do not understand optics/physics/mathematics well enough to represent the round earth side in this debate.
Where round earth is winning:
Astronomical charting of constellations has existed in mainstream since time of 200BC with Ptolemy having mapped 99% of skies, and in 1600 an obscure german astronomer added the few last unrecorded constellations at the southern axis to astronomical map. The astronomical maps of Ptolemy are spherical, where in a flat earth they should be merely a dome shape. Also, a test can be done to time lapse a video to show that the southern hemisphere is spinning around south axis/pole. You can observe far-southern constellations from southern hemisphere, and far-northern constellations from northern hemisphere. It is just that most recent advanced society has existed in northern hemisphere that folklore is centered on the northern hemisphere's constellations - however, if you lived in far-southern hemisphere you would not see them. To present flat earth counter argument to this: they say that you can in fact see north star even from far southern hemisphere. However, we have Rayzor in forum who says this claim is false. We are waiting for flat earther to refute Rayzor, but nobody has stepped up yet to be able to do so. others will bring counter argument that time lapsed videos of south pole are manipulated. There are thousands of such citizens who have made photos such as these, and any ordinary citizen can go to Chile to prove existance of south pole by viewing sky, and proof earth round (at least from astronomic perspective).
also, these are the red herrings:
* we would "fall off" if earth was sphere. Incorrect! you should say, we would would fall off if earth was spinning. however you can construct a model where earth is spinning or stationary! If you say that you would fall off spinning sphere, then why not also mention that you would fall off a 2 dimensional spinning disc? It seems both sides of debate often cherry pick...
* satellites: also a red herring.. it's plausible that if stuff can hang over in a sphere, that stuff could also hang over on a circle as well.
* moon landing, ISS, etc: also possible plausible in both scenarios.
guilt by association "cointelpro" arguments:
i use this term with sarcasm.. whether deliberately or accidentally, often debaters will play devil's advocate of other side of debate, and attach red herrings or other logical fallicies to opponents side of arguments to "disprove" them, when really they are just discrediting themselves and derailing debate. I have seen round earthers use this tactic by associating creationism (a negative connotation in today's society) to flat earthers while attaching creationism/bigbangism to round earth (a positive connotation, depending on viewpoint).. Or, from flat earth perspective, they often attach red herrings to round earth such as centrifical force, satellites, Nasa stuff, etc..